cbse sample papers

Class 12 (XII-Twelve) Syllabus NCERT Books Notes NCERT Solutions Answers Practice Questions

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NCERT Books for Class 12 all Subjects

Download NCERT Books for Class XII Mathematics, Physics, Chemistry, Biology and all other subjects in PDF form. All chapters of NCERT books are given as a separate links.

NCERT BOOKS FOR CLASS 12 MATHEMATICS

NCERT BOOKS FOR CLASS 12 MATHEMATICS – HINDI MEDIUM

गणित (भाग 1 तथा भाग 2)

NCERT BOOKS FOR CLASS 12 PHYSICS

NCERT BOOKS FOR CLASS 12 PHYSICS – HINDI MEDIUM

भौतिकी (भाग 1 तथा भाग 2)

NCERT BOOKS FOR CLASS 12 CHEMISTRY

NCERT BOOKS FOR CLASS 12 CHEMISTRY – HINDI MEDIUM

रसायन (भाग 1 तथा भाग 2)

NCERT BOOKS FOR CLASS 12 BIOLOGY IN PDF

NCERT BOOKS FOR CLASS 12 BIOLOGY IN HINDI MEDIUM

जीव विज्ञान

 

NCERT BOOKS FOR CLASS 12 ENGLISH (CORE)

Flamingo – Prose

Flamingo – Poetry

Vistas – Supplementary Reader

Class 11 (XI-Eleven) Syllabus NCERT Books Notes NCERT Solutions Answers Practice Questions

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NCERT BOOKS FOR CLASS 11 MATHS (ENGLISH MEDIUM)

NCERT BOOKS FOR CLASS 11 गणित (HINDI MEDIUM)

NCERT REVISION BOOKS CLASS 11 MATHS

NCERT BOOKS FOR CLASS 11 PHYSICS (ENGLISH MEDIUM)

NCERT BOOKS FOR CLASS 11 PHYSICS (HINDI MEDIUM)

भौतिकी (भाग 1 तथा भाग 2)

NCERT BOOKS FOR CLASS 11 CHEMISTRY (ENGLISH MEDIUM)

NCERT BOOKS FOR CLASS 11 CHEMISTRY (HINDI MEDIUM)

रसायन (भाग 1 तथा भाग 2)

NCERT BOOKS FOR CLASS 11 BIOLOGY (ENGLISH MEDIUM)

NCERT BOOKS FOR CLASS 11 BIOLOGY (HINDI MEDIUM)

जीव विज्ञान

NCERT BOOKS FOR CLASS 11 ENGLISH (CORE COURSE)

Hornbill (Core Course)

READING SKILLS
WRITING SKILLS

Snapshots (Core Course)

SUPPLEMENTARY READER

Class 10 (X-Ten) Syllabus NCERT Books Notes NCERT Solutions Answers Practice Questions

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NCERT Books for Class 10

CLASS 10 MATHS BOOKS (ENGLISH MEDIUM)

 

Class 10 Maths Books (Hindi Medium)

CLASS 10 SCIENCE BOOKS (ENGLISH MEDIUM)

 

Class 10 Science Books (Hindi Medium)

CLASS 10 SOCIAL SCIENCE NCERT BOOK ENGLISH MEDIUM

History (India and The Contemporary World – II)

 

Geography (Contemporary India – II)

Political Science (Democratic Politics -II)

Economics (Understanding Economic Development)

Click here to download Class 10 Social Science NCERT Solutions

CLASS 10 SOCIAL SCIENCE NCERT BOOK HINDI MEDIUM

 

इतिहास (भारत और समकालीन विश्व – II)

भूगोल (समकालीन भारत – II)

 

राजनीति विज्ञान (लोकतांत्रिक राजनीति -II)

अर्थशास्त्र (आर्थिक विकास की समझ)

CLASS 10 ENGLISH NCERT TEXTBOOK

First Flight

Chapter 1. A Letter to God
Chapter 2. Nelson Mandela:Long Walk to Freedom
Chapter 3. Two Stories about Flying
Chapter 4. From the Diary of Anne Frank
Chapter 5. The Hundred Dresses–I
Chapter 6. The Hundred Dresses–II
Chapter 7. Glimpses of India
Chapter 8. Mijbil the Otter
Chapter 9. Madam Rides the Bus
Chapter 10. The Sermon at Benares
Chapter 11. The Proposal

 

FOOTPRINTS WITHOUT FEET

Chapter 1. A Triumph of Surgery
Chapter 2. The Thief’s Story
Chapter 3. The Midnight Visitor
Chapter 4. A Question of Trust
Chapter 5. Footprints without Feet
Chapter 6. The Making of a Scientist
Chapter 7. The Necklace
Chapter 8. The Hack Driver
Chapter 9. Bholi
Chapter 10. The Book That Saved the Earth

INTERACT IN ENGLISH – LITERATURE READER
A Textbook for English Course (Communicative) – Friction (Prose)
POETRY

 

DRAMA
INTERACT IN ENGLISH – MAIN COURSE BOOK (MCB)
LONG READING TEXT – NOVELS

CLASS 10 HINDI NCERT BOOKS – COURSE A

Hindi – Course A – NCERT Book

KRITIKA – कृतिका
KSHITIJ – क्षितिज

CLASS 10 HINDI NCERT BOOKS – COURSE B

स्पर्श (पद्य)

 

स्पर्श(गद्य )

Sanchayan

 

NCERT BOOKS FOR CLASS 10 SANSKRIT

शेमुषी

व्याकरणवीथिः

Class 9 (IX-Nine) Syllabus NCERT Books Notes NCERT Solutions Answers Practice Questions

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NCERT Books for Class 9 All Subjects in PDF

Download NCERT books for class 9 all subjects for High Secondary (High School NCERT Books for UP Board Also) in Hindi Medium. All books are given below in separate chapters. NCERT solutions are also available to download in PDF form.

NCERT BOOKS FOR CLASS 9 MATHS – ENGLISH/HINDI/GUJRATI MEDIUM

 

 

 

NCERT BOOKS FOR CLASS 9TH MATHS (GANIT) – HINDI MEDIUM

 

NCERT EXEMPLAR BOOKS FOR 9TH CLASS MATHS – ENGLISH MEDIUM

 

Chapter 1: Number Systems
Chapter 2: Polynomials
Chapter 3: Coordinate Geometry
Chapter 4: Linear Equations in Two Variables
Chapter 5: Introduction to Euclid’s Geometry
Chapter 6: Lines and Angles
Chapter 7: Triangles
Chapter 8: Quadrilaterals
Chapter 9: Areas of Parallelograms and Triangles
Chapter 10: Circles
Chapter 11: Constructions
Chapter 12: Heron’s Formula
Chapter 13: Surface Areas and Volumes
Chapter 14: Statistics and Probability

Visit to NCERT Exemplar for class 9 Maths Main page

 

NCERT EXEMPLAR BOOKS FOR 9TH CLASS MATHS (GANIT) – HINDI MEDIUM

 

NCERT BOOKS FOR CLASS 9 SCIENCE – ENGLISH/GUJRATI MEDIUM

 

NCERT BOOKS FOR CLASS 9 SCIENCE – HINDI MEDIUM

 

NCERT BOOKS FOR CLASS 9 SOCIAL SCIENCE – ENGLISH MEDIUM

India and the Contemporary World – 1 (History)

 

Contemporary India – 1 (Geography)

Democratic Politics – I (Political Science)

Economics

 

NCERT BOOKS FOR CLASS 9 SOCIAL SCIENCE (सामाजिक विज्ञान) – HINDI MEDIUM

भारत और समकालीन विश्व – 1 (इतिहास)

समकालीन भारत – 1 (भूगोल)

लोकतांत्रिक राजनीति (राजनीति विज्ञान)

अर्थशास्त्र

NCERT BOOKS FOR CLASS 9 HINDI (COURSE A & B) – कक्षा 9 हिंदी

क्षितिज भाग 1 (‘अ’ पाठयक्रम)

गद्य-खंड

 

काव्य-खंड

कृतिका भाग 1 (‘अ’ पाठयक्रम)

संचयन भाग १ (‘ब’ पाठयक्रम)

स्पर्श भाग १ (‘ब’ पाठयक्रम)

गद्य खंड

स्पर्श भाग १ (‘ब’ पाठयक्रम)

काव्य खंड

 

 

NCERT BOOKS FOR CLASS 9 ENGLISH

Beehive

Moments – Supplementary Reader

 

NCERT BOOKS FOR CLASS 9 SANSKRIT

शेमुषी

व्याकरणवीथिः

Class 8 (VIII-Eight) Syllabus NCERT Books Notes NCERT Solutions Answers Practice Questions

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NCERT books for class 8

Download NCERT Textbook for 8th class Maths, Science, S. St. (History, Geography, Civics), Hindi & English in PDF form. Hindi Medium books are also given to download. Download 8 Maths Solutions App or 8 गणित के हल App, which work offline without internet

NCERT BOOKS FOR CLASS 8 MATHS – ENGLISH MEDIUM

NCERT BOOKS FOR CLASS 8 MATHS – HINDI MEDIUM

Download 8 Maths Solutions App or 8 गणित के हल App, which work offline without internet

NCERT EXEMPLAR BOOKS FOR CLASS 8 MATHS

 

NCERT BOOKS FOR CLASS 8 SCIENCE – ENGLISH MEDIUM

NCERT BOOKS FOR CLASS 8 SCIENCE – HINDI MEDIUM

 

NCERT BOOKS FOR CLASS 8 ENGLISH

Honeydew

It So Happened… – Supplementary Reader

NCERT BOOKS FOR CLASS 8 HINDI

Vasant

Durva

 

Bharat Ki Khoj

NCERT BOOKS FOR CLASS 8 SANSKRIT (रूचिरा – तृतीयो भागः)

NCERT BOOKS FOR CLASS 8 SOCIAL SCIENCE – ENGLISH MEDIUM

History (Our Pasts – III) (Part 1 & 2)

 

Geography (Resources and Development)

Civics (Social and Political Life – III)

 

NCERT BOOKS FOR CLASS 8 SOCIAL SCIENCE – HINDI MEDIUM

इतिहास (हमारे अतीत – III) (भाग १ और भाग २)

 

भूगोल (संसाधन एवं विकास)

सामाजिक एवं राजनितिक जीवन – III

Class 7 (VII-Seven) Syllabus NCERT Books Notes NCERT Solutions Answers Practice Questions

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NCERT books for Class 7 All Subjects (English & Hindi Medium)

The below mentioned list sows NCERT books for class 7 Maths, Science, Social Science, Hindi and English books in PDF form. English and Hindi medium books are given separately. You can read here or download for reference.

NCERT TEXTBOOKS FOR CLASS 7 MATHS – ENGLISH MEDIUM

 

NCERT TEXTBOOKS FOR CLASS 7 MATHS (गणित) – HINDI MEDIUM

NCERT EXEMPLAR BOOKS FOR CLASS 7 MATHS – ENGLISH MEDIUM

 

NCERT TEXTBOOKS FOR CLASS 7 SCIENCE – ENGLISH MEDIUM

 

NCERT TEXTBOOKS FOR CLASS 7 SCIENCE (विज्ञान) – HINDI MEDIUM

NCERT TEXTBOOKS FOR CLASS 7 SOCIAL SCIENCE – ENGLISH MEDIUM

History (Our Pasts II)

 

Geography (Our Environment)

Political Science

 

NCERT TEXTBOOKS FOR CLASS 7 SOCIAL SCIENCE (सामाजिक विज्ञान) – HINDI MEDIUM

हमारा पर्यावरण (भूगोल)

हमारे अतीत – 2 (इतिहास)
समकालीन और राजनितिक जीवन – 2 (राजनितिक विज्ञान)

NCERT TEXTBOOKS FOR CLASS 7 HINDI (DURVA AND VASANT PART 2)

 

दूर्वा भाग – २

वसंत भाग – २

बाल महाभारत कथा

 

NCERT TEXTBOOKS FOR CLASS 7 ENGLISH (HONEYCOMB & THE ALIAN HAND)

Honeycomb

The Alien Hand

Class 6 (VI-Six) Syllabus NCERT Books Notes NCERT Solutions Answers Practice Questions

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CBSE Class 6 (VI-Six) Science Syllabus

NCERT Books for Class 6 (VI-Six) PDF Download

NCERT Books for Class 6 All Subjects

NCERT TEXTBOOKS FOR 6TH CLASS MATHS (Text Book PDF / Notes  / NCERT Solutions)

NCERT BOOKS FOR CLASS 6 MATHS (गणित) – HINDI MEDIUM

NCERT TEXTBOOKS FOR 6TH CLASS MATHS EXEMPLAR PROBLEMS

NCERT EXEMPLAR FOR 6TH CLASS MATHS (गणित) – HINDI MEDIUM

NCERT TEXTBOOKS FOR 6TH CLASS SCIENCE

NCERT BOOKS FOR CLASS 6 SCIENCE (विज्ञान) – HINDI MEDIUM

NCERT TEXTBOOKS FOR 6TH CLASS HINDI

Vasant Bhag 1 (वसंत भाग 1)

Doorva Part – 1 (दूर्वा भाग 1)

 

बाल रामकथा – Bal RamKatha

NCERT BOOKS FOR CLASS 6 ENGLISH

Honeysuckle

A Pact with the Sun – Supplementary Reader

Click Here to Download NCERT Solutions Class 6 English in PDF

NCERT BOOKS FOR CLASS 6 SANSKRIT

रुचिरा – प्रथमो भागः

NCERT BOOKS FOR CLASS 6 SOCIAL SCIENCE

History – Our Pasts Part I

Geography – The Earth Our Habitat Part I

Political Science – Our social and political life Part I

 

NCERT BOOKS FOR CLASS 6 SOCIAL SCIENCE – HINDI MEDIUM

इतिहास – हमारे अतीत – I

भूगोल – पृथ्वी: हमारा आवास

CBSE Class 6 Science Syllabus Papers

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CBSE Class 6 Science:

                 CBSE Class 6 Science syllabus can be widely classified as follows:

They are:

  1. Food
  2. Materials
  3. The world of living
  4. Moving things, people and ideas
  5. How things work
  6. Natural resources

The above topics are in detail below:

 

  • Food:

         Any typical food which we eat contains different ingredients which come from different sources such as plants and animals. Plants are the sources of vegetables, seeds, oil, fruits, etc whereas animals are the sources of dairy products, milk, meat and eggs.

       The subtopics which are covered under this chapter are Components of food, sources of food and cleaning food.

Sources of food:

                 This topic covers what are the various sources of food that animals depend upon. What do the animals eat? Plant parts and animal products are the some examples of sources of foods.

As we all know, food is an essential thing for all kinds of living organisms. Every organism depends on other organism for making their food. For example, larger animals depend on smaller organism for their food, similarly human beings depend on animals for their food.

Plant food products:

                 Plant food products are the different types of food we get from the plants. Plant is the major source of food for vegetables, fruits, seeds and oils. Few of those examples are

Roots: We consume plant roots in the form of carrot, turnips, radish and beetroot.

Flowers: We consume flowers in the form of cauliflower, flowers of pumpkin and few kinds of roses are used to make edible oils.

Stem:

         We eat stem related source of foods from plants such as coriander, sugarcane, potatoes, etc.,

Fruits:

             We get many different types of fruits like fleshy or dry fruits. Fruits like mango, guava, orange, and apple are the important source of food from the plants.

Seeds:

           We eat grains, pulses, ground nuts which are the important sources of foods in the form of seeds from the plants.

Leaves:

       We eat leafy vegetables such as spinach, cabbage, curry leaves which are rich in calcium and vitamins.

Animal food products:

      Just like plants, animals also make many kinds of foods that are very helpful for the human beings.

Milk:

           Animals such as cow, goat, and buffalo are tamed in their own farms to produce milk from them. This is a rich source of food which is rich in calcium.

Eggs:

           Birds like hen, duck are tamed and reared in their poultry farms for their eggs which is rich in protein.

Meat:

       Animals such as goat, cow, pig, duck, sheeps are tamed to get flesh from them which is called as meat.

Dairy products:

         Not only milk, but also other dairy products are made from the milk of animals such as cow, buffalo, donkey, goat, etc.,

Sea food:

       Sea foods like fish, prawns, and crabs are also highly used foods for the human consumption.

Honey:

        This is a product which is obtained from the Honey bee. Honey collects nectar from various fruits and flowers. Such nectars are collected together to form honey.

Components of food:

       Any healthy food consists of six important nutrients such as carbohydrates, fats, vitamins, protein, minerals and water. These nutrients are much necessary to perform various metabolic activities.

Carbohydrates:

               Carbohydrates are the compounds of carbon, hydrogen and oxygen and provide instant energy for the human body. Examples: rice, jowar, grains, etc.,

Proteins:

           They are formed by the compounds such as carbon, hydrogen, oxygen and nitrogen. Protein is required to repair and damage the broken cells in the human body. Example: egg, milk, cheese, etc.,

Fats are made up of carbon, oxygen and hydrogen. Fat protects the skin from the rapid loss of heat. Example: Cheese, butter, oil, ghee Vitamins are the chemical substances that help in maintaining a healthy body. Example: Lemon, oranges, tomatoes, etc.,

Examples:

  1. Tiger is _______ animal since it eats only meat

Answer: carnivore

  1. Name two foods that are rich in starch.

Answer: Butter and Groundnuts

 

  • Materials:

         This chapter covers the various topics such as different types of cloth materials, types of plant fibres, and some concepts such as why candle shortens when lighten up, how does salt gets dissolved in a cup of water, etc.,

Fibres:

           Cloth is a basic necessity for any human being to protect his body from the external environment. Such cloths are made up of different fabric materials such as wool, fibre, silk, leather, etc.,

Fibres are of two types such as natural fibre and synthetic fibre. Natural fibre are made from the natural sources of plants and animals such as cotton, jute, silk and wool. Synthetic fibre are man-made fibres which are not obtained from any plants and animals. Example: Nylon, polyster, etc.,

Properties of materials:

           Every material has different property and nature. For example:

Metals:

   Most of the metals are lustrous and shiny in nature. Thus, they are used in jewellery making. For example: Gold, silver, etc.,

Cotton:

               The materials such as cotton or sponge are soft by nature. Thus they are used in making sarees, toys and other soft materials.

Plastics:

           The nature of material is light and transparent sometimes. Thus, they are used in making bottles, jugs, play sets, etc.,

Wood:

         This type of materials is opaque in nature which do not allow light to pass through them. Thus, cupboards are made up of wood.

Examples:

  1. State true or false:
  • Is yarn made up of fibres?

             Answer: True

  1. Name any two items that are made from the coconut fibre?

Answer: Bags and ropes

 

  • The world of living:

             This chapter covers the topics such as living and non-living beings characteristics, habitat of the living organisms and morphological structure and function of plants, bones and skeleton system of human beings.

Getting to know the plants:

                 Plants can be classified into different types according to their size and nature. They are as

Herbs:

         Herbs are usually short and have a short period of life. They are mainly used in medicine to cure specific diseases.

Shrub:

             This is taller than herb which lives for longer years. Examples are sunflower, rosemary, etc.,

Tree:

           This is a woody plant that has many stems and branches. They prevent soil erosion, maintain carbon dioxide content in the air, and provide us wood and other materials to build up huts and houses. Creepers are the weak plants which cannot stand straight. They grow horizontally on the ground and live for very short period of time.

Body movements:

               Human beings are able to move from one place to another with the help of their muscles, joints and limbs. Thus, the parts in detail

Joint:

       Joint is a point at which two separate bones meet. There are three types of joints in the human beings such as fixed or immovable joints, slightly movable joints and freely movable joints.

Bones and skeleton:

           Bones provide support to the structures in the body whereas Skeleton system of a human body is an internal framework of all the bones and cartilage in the human body.

Living organisms and the surroundings:

                  There are different types of atmosphere and seasons to which all kinds of living organisms must adapt.

Habitat:

               Habitat of an organism is its immediate surroundings. There are two types of habitat such as Terrestrial habitat (Forest, grasslands, desserts, etc) and Aquatic habitat (Freshwater, ponds, lakes, etc.)

Adaptations:

             The ability of any organism to adjust itself to the type of the surroundings is called as adaptation.

Characteristics of a living organisms:

         All kinds of living organism require certain characteristics of life. They are they require food to exhibit growth, need to move, need to excrete, respire, reproduce and die.

These are the basic characteristics of any kind of living organism.

Examples:

  1. State true or false?
  • The movement and locomotion of all kinds of animals are exactly same?

Answer: False

  1. Which of the skull bones are movable

Answer: Lower jaw

 

  • Moving things, people and ideas:

            This covers the topics such as need to measure the length and motion as change in the position of time.

Measuring length and its accuracy:

                 Length is a basic physical quantity which can be measure with the help of a scale and ruler. Length of a straight line can be measured with the help of a ruler whereas the curved line can be measured with the help of a non-stretchable string. In these ways you can measure any kind of object accurately.

Transportation and distances:

               Moving from one place to another is called as transportation. Before walking was only means of transport which later developed into trains, cars, buses as the means of transportation. Nowadays, any kind of distances and lengths are covered with help of different means of transports.

Examples:

  1. One meter ___ in cm.

Answer: 100 cm

  1. The height of a person is 1.65m. Express in cm and mm.

Answer: 165 cm and 1650 mm

 

  • How things work:

       This chapter covers the topics such as conductors, insulators, components of an electric current, magnet, poles of an magnet, etc.,

Electric circuit:

             Electricity basically needs a path to flow from the positive terminal to negative terminal of an electric cell. A connection which forms a path for this flow of electric current is called as electric circuit.

Conductors and insulators:

                   Materials that do not allow electricity to pass through them is called as insulators whereas materials which allow electric current to pass through them is called as conductors.

Example for insulators: Distilled water which means water at its purest form

Example for conductors: Tap water which means water with impurities

Properties of a magnet:

                   Substances which possess the property of attracting iron is called as magnet. The two ends of a magnet is called as poles which is called as north and south pole.

The properties of a magnet can be stated below as:

  1. A Magnet attracts magnetic materials towards itself
  2. Unlike poles attract each other whereas like poles repel each other
  3. When a bar magnet is rubbed over an iron bar, it changes the iron bar into magnet.

Examples:

  1. A device that is used to break an electric circuit is _____

Answer: Switch

  1. Paper is not a _______ material.

Answer: Magnetic

 

  • Natural resources:

                 This chapter covers the topics such as natural calamities, conservation of water, forests, importance of water, etc.,

Natural calamities:

             Natural calamities such as heavy rainfall, thunder, cyclone, flood and drought are the uncontrolled conditions which affect the areas of earth.

Floods:

       Floods cause heavy loss to the human beings by uprooting crops, shelter, trees and so on.

Rainfall:

           A heavy rainfall may result in flood which is as said above is a disastrous natural calamity.

Drought:

             Drought is condition which has made the areas dry without rainfall and water. This is also a serious issue which may cause more deaths in the affected areas.

Conservation of water:

                 Water is a basic and important source for life and no life exist without water. Thus waters must be conserved in the following ways such as

  1. Avoid unnecessary water wastage
  2. Drinking water should not be used to water the plants
  3. Water bodies should be kept clean and must not be polluted.
  4. Destruction of trees must be avoided
  5. Every house must have implemented rain water harvesting system

     Examples:

  1. Water drops appears on the outer surface of a glass containing cold water. This process is called as ________

Answer: Condensation

  1. Which gas in the atmosphere is essential for the respiration?

Answer: Oxygen

       Thus, above are the topics which are covered in the syllabus of CBSE Class 6 Science.

CBSE Class 1 Mathematics Syllabus

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CBSE Class I Mathematics:

CBSE Class 1:

             CBSE Class 1 students have various subjects like Mathematics, Science, English, Computer and Hindi. Among this, let us check the details about the CBSE Mathematics below:

 

Chapters covered in CBSE Class I Mathematics:

                         Math is a very important subject to trigger the brain right from the childhood. Students get familiar with this subject right from their younger age through counting and number systems. Keeping this in mind, CBSE board has developed suitable Mathematics syllabus for every Classes. Through CBSE Class I Math, students get adapted to a sequential system of learning math which can make them to learn it comfortable. With few small examples and simple exercises, CBSE trains even the small kid to brilliantly solve the mathematical questions.

Thus, let us check the chapters covered in the CBSE Class 1 Mathematics here:

  • Shapes and Spaces:

     Students are trained to find out various shapes and sizes. In addition to this, they are trained to know the special relations such as Top, bottom, under, above, near, far, before, etc.

Example:

               Shapes like Hexagon, square, pentagon, cube, oval and various other shapes are trained through real time objects.

Exercises for this chapter:

  1. Students have to collect different objects from the surroundings such as stones, pebbles, cones, pipes and name their shapes in their notes.
  2. They are taught to observe the effects caused due to rolling and sliding of the shaped objects.
  3. Sorts and finds out the 2D objects which are made out of card board.

 

  • Number system:

     Developing the knowledge in counting and numbering systems. They are taught to count from one to hundred at this stage.

Exercises for this chapter:

  1. Counts the number of toys, dolls which are in their surroundings.
  2. Recognizes and speaks numbers from 1 to 9.
  3. Forms number sequence from 10 to 20.
  4. Knows the difference between group of tens and ones in numbering system.
  5. Writes the numerals from 11 to 19. Also, spells the numerals.

 

  • Addition and Subtraction:

             Addition and Subtraction is rather an important part in mathematics. Students are taught to add and subtract using the real objects and pictures. Learns to add and subtract the numbers upto 20. Knows the importance of Zero in addition and subtraction.

      For example:

       5+5=10

       5-5=0

 

  • Telling time:
  1. Knows the importance of time. Learns to check the events occurring earlier and later.
  2. Introduction to time. Difference between morning, afternoon, day and night.
  3. Reading the clock.
  4. Understanding which activities takes longer time.
  5. Difference between analog and digital clocks.
  6. Sequencing student activities according to the time occurrence.

Examples:

  1. The time now is 8 o’ Clock.
  2. 1 minute is equal to 60 seconds.
  3. 60 minutes is one hour.

 

  • Days, weeks, months patterns:

               Students are taught the basic things in Days, months and week patterns.

Exercises:

  1. Students are taught that there are 12 months in a year, 4 weeks in a month and each week has 7 days.
  2. Learn the names of the months and days.
  3. Exercises given to identify the month and day.

               Example:

  1. The day after Sunday is Monday.
  2. Number of days in the month of January is 31.

 

  • Money:

           Students are trained to identify common currencies and notes. Learns the importance of currency and different values of Indian currencies. Adds and subtracts few sums of money.

Example:

  1. Father has a balance of 10 rupees after he purchased shampoo for Rs.10 from the total money Rs.20.

20-10=10

 

  • Measurement:
  1. Differentiates between near, far, thick, thin, longer, shorter, high and low.
  2. Exercises are given to find out the longer and shorter distance, higher and lower prices, thicker and thinner persons, etc.

                Example:

  1. Meera is shorter than Latha with pictures.
  2. Milk is costlier than egg with pictures and numbers.

 

  • Data handling:
  1. Counting letters in a name.
  2. Grouping names with the same number of letters
  3. Counting and recognizing shapes, etc.,

                   Example:

  1. Total number of letters in “welcome” is 7.
  2. Sample of 4 letter words are “Good”, “Best”, “Baby”, etc.,
  3. There are 3 squares and 2 ovals in this picture.

These are the topics which are covered for the Class 1 CBSE students.

 

CBSE Class 3 Mathematics Syllabus

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CBSE Class 3 Mathematics:

              When compared to CBSE Class 3, CBSE Class 2 Mathematics covered various simple topics on Addition, subtraction, multiplication without carry, place value in numbering system, simple division, etc., But in CBSE Class 3, next level mathematics is taught to enhance and trigger the brain of the child. For this, they have included the portions just similar to that of Class 1 and Class 2 but in little higher level. Among all the subjects of CBSE Class 3 like Mathematics, Science, Hindi and English let us check out the syllabus of Mathematics below.

 

CBSE Class 3 syllabus:

             They cover similar syllabus just like that as Class 2 and Class 1.

  • Numbers:

           Children are taught to write the series of numbers up to 9999 in Class 3. Also, they are trained to pronounce and write the compact and expanded form of such numbers.

Topics covered:

  1. Compact and expanded forms of numerals
  2. Roman numerals
  3. Ascending and descending order of the numbers
  4. Rounding off
  5. Place value
  6. Equivalent numerical names

        Examples:

  1. Fill up the missing numerals:
  • 200 _ _ _ _ 205
  • 345_347_ _ 350
  • 34_ _ _ 38_ _ 41

        Answer:

  • 200 201 202 203 204 205
  • 345 346 347 348 349 350
  • 34 35 36 37 38 39 40 41
  1. Write the equivalent number names for the following:
  • 199 = One hundred and ninety nine
  • 214 = Two hundred and fourteen
  • 3450 = Three thousand four hundred and fifty
  1. Write the equivalent numerals for the number names
  • Three hundred and sixty six = 366
  • Four hundred and thirty five = 435
  • Two thousand six hundred and thirty five = 2635
  1. Roman numeral VI ______ than VIII
  • < 
  • > 
  • =

               Answer: <

  1. How would you write ten in roman letter?
  • X
  • XII
  • V

                 Answer: X

 

  • Addition and Subtraction:

                 Addition and Subtraction are rather important chapters for a growing child which triggers his/her brain to solve the questions. In class 1 and class 2, addition and subtraction were little simpler with simple two digit and three digit additions and simple word problems. But in class 3, next level of addition such as four digit addition, subtraction with or without borrowing, addition and subtraction word problems are covered.

Examples:

  1. Answer the following:
  • 8789 + 5674 = ?
  • 567 + 4563 = ?

    Answer:

  • 14463
  • 5130
  1. Find 6090 – ______ = 5590

    Answer:

  • 500

 

  • Multiplication and Division:

         Covers the topics such as counting using rows and columns, multiplication tables from 2 to 7, multiplying by 1, multiplying by 0, grid multiplication and word problems in multiplication. In division it covers, division by 10 and 100, division with two digit number, multiplication and division mixed problems, division word problems, etc.

Examples:

  1. 500 pencils are shared among 5 students of the classroom equally. How many pencils did each one get?

Answer: 100

  1. There are 20 bags of apples. Each bag contains 100 apples. Totally how many apples are there?

Answer: 2000

 

  • Fractions:

         Fractions are the important part of mathematics and it is very important to understand it clearly. Fraction comes as proper and improper fraction. The terms numerator and denominator are very important in the concepts of fraction.

Numerator = Number that is above the fraction line. Example: 2 in 2/3

Denominator= Number that is below the fraction line. Example: 3 in 2/3

Proper fraction has numerator smaller than the denominator whereas improper fraction has numerator larger than denominator. An improper fraction can be converted into a mixed fraction having a proper fraction and integral part. Fractions can be added, subtracted, divided and also multiplied.

Examples:

  1. Find out the fraction of vowels in the word “GREAT”?

Answer:

2/5

  1. There are totally 5 glasses of water in the table. Geetha drank 3 glasses of water. What is the fraction of water did geetha drink?

Answer:

3/5

 

  • Rupees and paise:

     Students are taught how to spend their own money and how to add, subtract, multiply and divide with their own money.

Examples:

  1. 6 Rupees is equal to _______ paise

Answer: 360 Paise

  1. 35 is equal to ______ paise

Answer: 575 Paise

  1. 675 paise is equal to _____ rupees

Answer: Rs.11.25

 

  • Time and Date:

         Topics covered such as Time taken to finish a task, puzzles for young minds, understanding the calendar, reading the clock and differentiate between AM and PM, etc.

Examples:

  1. How many rounds does an hour hand complete in a day?

Answer: 2 rounds

  1. What is the exact time taken by the minute hand to move from one number to the next number?

Answer: 5 minutes

 

  • Shapes and their properties:

               Topics covered such as different shapes and sizes, properties of shapes, edges and corners, vertices and surface, review of shapes and sizes, etc.,

Examples:

  1. Which of the following options are measured in cms and m?
  • Length of the banana
  • Height of your father
  • Distance from home to office

         Answers:

  • In cms
  • In cms
  • In meters
  1. Mention the length of the objects surrounding you:
  • Pen
  • Sharperner
  • Spoon

             Answers:

  • 10 cms
  • 3 cms
  • 8-9 cms

 

  • Measurement of length, mass and capacity:

              The basic things like standard unit of length, standard unit of mass, standard unit of capacity, converting meter to centi-meter, milli-meter and kilometer, etc are taught in this section. Students are given the basic understanding that the length of the pencil is measured in centi-meters whereas the distance between two places are measured in meters. Similarly, they are also taught how to measure the mass (in terms of kgs) and capacity (in terms of ml and l).

Examples:

  1. 18 L = _____ ml

Answer: 18000

  1. My mother is making noodles for dinner. Each noodles packet weighs 500g. How many grams of noodles will be there in 6 packets.

Answer: 3000 grams

  1. Add 85m 25cm and 56 m 44 cm and write the answer:

Answer: 141m 69 cm

 

  • Smart charts:

             Pictorial representation of collection of data is called as charts. Topics which are covered are drawing simple charts with two or multiple columns, reviewing simple graphs, pictograph, etc.

Examples:

  1. Answer the questions according to the datas given below:
  • Painting : 10

Dancing: 8

Music: 5

Craft: 15

Cycling: 13

Gardening: 14

Stamp collection: 10

Reading: 9

     Questions:

  1. Which is the most popular hobby?

Answer: Craft

  1. Which is the least popular hobby?

Answer: Music

  1. What is the difference between the number of students interested in Stamp collection and Dancing?

Answer: 2

 

  • Play with patterns:

             This section covers topics such as understanding pattern around us, detecting the number patterns, arranging in alphabetical order, skip counting, growing patterns and even odd patterns.

Examples:

  1. Arrange the following names in alphabetical order:
  • Abinay
  • Xavier
  • Harish

               Answer:

  • Abinay
  • Harish
  • Xavier
  1. Complete the following numerical patterns:
  • 98,198,298,398,_

                 Answer:

  • 98,198,298,398,498

Thus, these are the topics covered in CBSE Class 3 Mathematics.

CBSE Class 2 Mathematics Syllabus

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CBSE Class 2 Mathematics:

                     Just like CBSE Class 1 Subjects, Class 2 includes subjects such as Mathematics, English, Hindi and others. In Class 1, students are taught some basic topics in all the above subjects whereas in Class 2, subjects are going to get little deeper than Class 1.

                    Among all the subjects like Mathematics, English, Science and Hindi let’s get a deeper look into “Mathematics” and its syllabus for CBSE Class 2 students.

 

Syllabus for CBSE Class 2 Mathematics:

  • Numbers:

                Understanding the sequence of numbers, names of the number and grouping the numbers. The topics which are covered under the “Number system” are:

  • Introduction to counting the numbers in groups
  • Looking and guessing the numbers
  • Formation of things in group
  • Concept of Greater than(>) and Lesser than(<) symbols
  • Order of numbers
  • Names of the numbers (up to 9999)
  • Formation of ascending/descending order of numbers.
  • Learning about odd and even numbers
  • Comparing numbers (After/before/in between)

 

      Examples:

  1. Write the below numbers in words:
  • 33
  • 406
  • 345

     Answers:

  • Thirty Three
  • Four hundred and Six
  • Three hundred forty five
  1. Circle the numbers that are more than 234:
  • 235
  • 233
  • 222

     Answers:

  • 235
  1. Arrange the following numbers in ascending and descending order:
  • 45,78,13,9,5,64,79,109 (in ascending order)
  • 67,87,34,12,09,7,1,45 (In descending order)

     Answers:

  • 5,9,13,45,64,78,79,109
  • 87,67,45,34,12,09,7,1
  1. Write the numerals for the following number names:
  • Forty six
  • Sixty seven
  • Thirty two

    Answers:

  • 44
  • 67
  • 32
  1. Fill in the blanks:
  • 50 + 20 + 6= _ + 20 + 50
  • 12 + 13 + 4 = 13 + _ + 12
  • 7 + 5 + 7 = 7 + 7 + _

    Answers:

  • 50 + 20 +6= 6 +20 +50
  • 12 + 13 + 4= 13 + 4 +12
  • 7 + 5 +7= 7 + 7 + 5

 

  • Place value:

                Students have to know the importance of the place values in the numbering system and they should be able to identify whether the place value is “Ones”, “Tens” or “Hundreds”.

For example, in a two digit number, the position of each digit gives its values. In 25, it has 2 tens and 5 ones.

Examples:

  1. Write the place value for the following numbers:
  • 235
  • 789
  • 603

            Answers:

  • 2 is in hundreds place
  • 8 is in tens place
  • 3 is in ones place
  1. Compete the following:
  • 5 tens + 2 ones
  • 4 tens + 4 ones
  • 5 hundreds + 3 tens + 2 ones

            Answers:

  • 52
  • 44
  • 532

 

  • Skip counting:

       Skip counting means finding the next number in the series. For example, in the series of 10, 20, 30…the next number which comes is “40” and “50” respectively.

Examples:

  1. Fill up the blanks with skip counting:
  • 5,15,20…..50?

                 Answers:

  • 5, 15, 20, 25, 30,35,40,45, 50.
  1. Fill up the following series:
  • 2, 12, 22,…?

                       Answers:

  • 2, 12,22, 32,42,52

 

  • Addition and Subtraction:

                 In CBSE Class 1, students would have learnt only basics in addition and subtraction. But in Class 2, students are taught to solve word problems in addition and subtraction. In Class 2, students learn to add or subtract a number using zero, observes commutative property of addition through patterns, solves problems described through pictures and verbal description. Other topics covered are Addition with carry over, adding 4 digit numbers, adding two digit numbers, addition word problems, etc.,

Examples:

  1. 10 -10=0
  2. 9-2=7
  3. 435+100=535

 

  • Multiplication and Division:

         The topics which are covered here are multiplication without carry, multiplication tables of 2,3,4,5,6, etc., skip counting to multiply and simple division.

Examples:

  1. Fill up the following:
  • 5 * 10 = _
  • 4 * 3= _
  • 3 * 9 =_

     Answers:

  • 50
  • 12
  • 27
  1. 450 * 10 = 4510
  2. 16 % 4 =4
  3. 25 % 5=5

 

  • Money:

           Learns to identify important currencies, coins, etc., Adds and subtracts money through mental arithmetic.

Examples:

  1. Write the amount in words:
  • 50 = Seventy six rupee and 50 paisa
  1. Write the amount in figures:

Five hundred and sixty six rupees and 10 paisa = Rs.566.10

 

  • Time and date, calendar:

            Students are taught basic things about year, month, days. They should have a clear understanding that 12 months are in a year, 7 days form a week and 4 week for every month, etc.,

Examples:

  1. Differentiate the months and days below:
  • January
  • Monday
  • Tuesday

        Answer:

  • January is the name of the month
  • Monday is the name of the day
  • Tuesday is also the name of the day
  1. The longer hand of the clock is called as Minute hand.
  2. A leap year has 366 days.
  3. Which month comes before March? February
  4. Which is the first month of the year? January

 

  • Basic shapes, symmetry in everyday life:

  Learns to identify 3-d shapes of rectangle, triangle, cuboid, cylinder, cone and sphere.

Examples:

  1. A closed figure with four equal sides is said to be a Cube
  2. A bangle is in the shape of

 

  • Lines:

           Learns to identify the differences of vertical, horizontal and straight lines.

Examples:

  1. Please identify the number of vertical lines in the given picture.

 

  • Word problems based on Addition and Subtraction:

Along with solving small problems in addition and subtraction, students are trained to solve word problems in addition and subtraction areas.

Examples:

  1. Latha has 25 apple sweets and 15 orange sweets. Totally how many sweets does she have?

        Answer:  40

  1. Seetha has 20 stamps out which she gave 5 stamps to rama. Now, how many stamps does seetha have?

          Answer:  15

 

  • Measurement of Mass, Length, capacity:

     Learns to measure the lengths in units, measure the mass in terms of internal volume, and compares one or more objects with their weights.

Measurement of Mass:

          Using the formulas of simple balance calculates the weight of given objects. Also differentiates between heavier and lighter objects.

Measurement of Length:

          Using simple units to measure length, calculates an objects Length.

Measurement of Weights:

         Calculates volume of the containers using simple formulas of calculating volume.

Examples:

  1. Length of the boundary of the wall is measured in
  • m
  • Kg
  • l

           Answers:  M (Meter)

  1. A teaspoon of medicine is measured in
  • l
  • ml
  • cm

             Answer:   ml (milli litre)

  1. Your weight is measured in
  • g
  • kg
  • l

            Answer:  Kg (Kilo gram)

Thus, above are the syllabus covered under the CBSE Class 2 Mathematics.

 

 

CBSE Class 10 Science Syllabus

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CBSE Class 10 Science:

             CBSE Class 10 Science syllabus is divided into two terms such as Term 1 and Term 2. Term 1 includes the following topics such as:

Term 1:

  • Chemical substances- Nature and behavior
  • World of living
  • Effects of current
  • Natural resources

Term 2 includes topics such as:

  • Chemical substances-Nature and Behavior (Continued)
  • World of Living (Continued)
  • Natural Phenomena
  • Natural Resources (Continued)

The above syllabus in detail are:

 

  • Chemical Substances- Nature and Behavior:

             In first Term the above chapter covers the topics such as Chemical reactions, acids, bases and salts, metals and non-metals. In the second Term it covers the chapter such as Chemical substances-Nature and Behavior, Periodic classification of elements.

Chemical reactions:

               This chapter explains about the chemical reactions that occur naturally on any given substance. For example, when milk left at the room temperature during summers will turn it from its original nature, why grapes gets fermented and how foods are digested in our body. Thus, a chemical reaction can be defined as a process of conversion or transformation of a set of substances into another form. It is represented by a chemical equation which represents reactants, products and their physical states symbolically.

Any chemical equation is always in a balanced state so that the number of atoms of each type of reactant remains the same on the reactant and product sides of the equation.

The major topics which are covered under this chapter are

  • Chemical equations and balanced chemical equations
  • Types of chemical reactions
  • Effects of oxidation in everyday life
  • Understanding and writing chemical reactions

       Acids, Bases and Salts:

                             This is a chapter which indicates the different taste that occurs in the food substances

         because of the acids and bases.

       Some of the examples of acids and bases reactions are

  1. Acids when reacts with a metal, hydrogen gas is evolved and a corresponding salt is formed.
  2. When an acid reacts with the metal carbonate or metal hydrogen carbonate, it gives the corresponding salts, carbon dioxide and water.

A scale called as pH scale is used for testing the strength of the acid or alkali. This chapter also covers various topics on preparation and properties of beaching powder, washing soda, plaster of paris, common salt and baking soda.

Metals and non-metals:

                     Metals are ductile, malleable and are good conductors of heat and electricity. Except the metal Mercury, almost all metals are solids at the room temperature. The extraction of metals from their ores and then refining them for use if known as metallurgy.

                    Non-metals have the properties just opposite to that of the metals. They are neither ductile nor malleable. They are bad conductors of heat and electricity except for graphite which conducts electricity.

Periodic classification of elements:

           Elements can be classified on the basis of the similarities in the properties. Elements can be arranged in an increasing order of atomic masses and according to their chemical properties. Thus, for reference a periodic table is formed mentioning every possible elements.

        Examples:

  1. Give an example of the metal which
  • Is a liquid at the room temperature
  • Is a best conductor of heat
  • Is a poor conductor of heat
  • Can be easily cut with knife

           Answer: 

  • Mercury
  • Silver
  • Lead
  • Sodium
  1. Why curd and sour substances must not be kept in the brass and copper vessels?

Answer: Brass and copper vessel contains copper which reacts with the acids found in the curd or other sour substances. Thus, this reaction forms soluble salts which are poisonous in nature making curd unfit for the consumption.

  1. Why sodium is kept immersed in kerosene oil?

Answer:  Sodium reacting with oxygen catches up fire when kept in open place. Thus, sodium is always immersed in kerosene oil to avoid such accidents.

  1. Why should a magnesium ribbon be cleaned before burning in air?

Answer: To remove the protective layer of basic magnesium carbonate from the surface of magnesium ribbon.

  1. Write the balanced equation for the following:
  • Hydrogen + Chlorine ->Hydrogen Chloride    

               Answer: H2+ Cl2->2HC

 

  • World of Living:

             This is a chapter which is covered in both first Term and second Term. In first term the topics which are covered are Life processes, control and co-ordination in plants and animals. In second term, the topics which are covered include Reproduction, Heredity and Evolution.

Life process:

             Life processes that take place in both plants and animals are covered under this topic. The topic life process includes nutrition, respiration, transportation, excretion in plants and animals. Life process in animals include Digestive system which explains the role of digestive enzymes in the digestion of food. Respiratory system is divided into two types as Aerobic respiration and anaerobic respiration. Aerobic respiration occurs in the presence of oxygen and by-products carbon dioxide, water and energy whereas Anaerobic respiration occurs in the absence of the oxygen and by products are ethanol and carbon dioxide.

             Excretory system in animals is the taken place by the functions of nephron which is responsible for purification of blood and urine formation. Just like the life processes in animals, life process in plants is covered under this chapter. Topics such as Transportation of water and minerals, mechanism of Photosynthesis, Respiration during day and night, Excretion in plants, nutrition in plants and so on.

Control and coordination in animals and plants:

           When humans step out in the bright sunlight, they partly close their eyes due to the excessive brightness of sunlight. In addition to this, they may start sweating as the temperature rises. These are called as the coordinated responses to stimuli. This not only occurs in humans but also in plants and animals.

Reproduction:

       This chapter covers the reproduction process in both plants and animals. It covers many concepts like budding, fragmentation, spore formation and sexual reproduction in humans and plants.

Heredity and Evolution:

              This chapter deals with the relationship between our physical appearance and resemblance to our family members. Evolution can be defined as change in the characteristics of living organisms over generations.

Examples:

  1. Name the excretory unit of the kidney?

Answer: Nephron

  1. Explain the process of Photosynthesis in plants:

Answer: Photosynthesis is a process in which plants use sun light, chlorophyll, carbon dioxide and water to synthesize food.

  1. Why does a plant cool the atmosphere? What is that term called as?

Answer: Transpiration

 

  • Effects of Current:

                     This chapter covers the basic topics under “Electricity” such as Ohm’s law, Resistance, Resistivity, Parallel combination of resistors and applications in daily life, electric power, heating effects of the current and its everyday applications, magnetic effects of electric current, etc. The region around the magnet where its influence or attraction is felt is called as the magnetic field of the magnet.

Examples:

  1. Define the unit of the current?

Answer: SI unit of the electric current is Ampere

  1. List any one property of the magnetic lines of force?

Answer: No two magnetic field lines intersect each other

 

  • Natural Phenomena:

         This covers the topics such as reflection of the light by the curved surfaces, mirror formula, concave mirror, convex mirror, reflection and refraction, focal length, principal focus, laws of refraction, etc. Reflection means change in the path of the wave when the bounce-off a barrier. Refraction of the waves means change in the direction of waves when they pass from one medium to another.

Examples:

  1. The radius of the curvature of the spherical mirror is 20 cm. What is its focal length?

Answer: 10 cm

  1. Name the mirror which can give you an erect and enlarged image of an object?

Answer: Concave mirror

 

  • Natural Resources:

                 In First Term it covers the topic such as Sources of energy and in the second Term it covers the topics such as regional environment, our environment and management of natural resources.

       Sources of energy:

                 This chapter is based on the concept that “Energy can neither be created nor be destroyed but can be converted to one form to another”.

      Management of natural resources:

                 This covers the topics such as how to conserve and manage the natural resources such as Forest, wildlife, water and mineral. It explains about three R’s such as Reduce, Recycle and Reuse.

      Our environment:

                 It is a study of living things, non-living things, ecosystem, loss of energy in the environment and large number of environmental problems. An ecosystem is a study of interaction between living and non living organisms. Environmental problems arise due to non-biodegradable waste generated by the humans such as plastics, detergent, dyes which get settled into the soil and water bodies and harm our environment.

       Examples:

  1. What is a good fuel?

Answer: A good fuel is that which releases more heat during burning but do not cause any environmental problems.

  1. What are the qualities necessary for a good source of energy?

Answer:

  • It should be easily available
  • It should be easy to store and transport
  • In should not cause any environmental problems
  • It should be economical
  • It should have high calorific value
  1. In what way does a biodegradable substance effect the environment?

Answer: It gives foul smell, thus causing air pollution

  1. Examples for biodegradable and non biodegradable substances?

Answer:

Biodegradable: Vegetable waste, cotton, paper

Non-biodegradable: Plastic, glass and polythene

Thus, above are the topics which are covered under the syllabus of CBSE Class 10 Science.

 

CBSE Class 10 Mathematics Syllabus

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CBSE Class 10 Mathematics:

                     Just like the CBSE Class 9 Mathematics, CBSE Class 10 Mathematics syllabus is also divided into two terms such as Term 1 and Term 2. Term 1 covers the following syllabus such as:

  • Number systems
  • Algebra
  • Geometry
  • Trigonometry
  • Statistics

Term 2 syllabus are:

  • Algebra (Continued)
  • Geometry (Continued)
  • Trigonometry (Continued)
  • Probability
  • Coordinate geometry
  • Mensuration

The syllabus are in detail below:

  • Number systems:

                 This includes topics such as proof of irrationality, decimal representation of rational numbers, Fundamental theorem of Arithmetic, Euclid’s division lemma, etc.,

Fundamental theorem of arithmetic:

                 Any integer which is greater than one is either a prime number or can be expressed as a product of prime numbers and this factorization is unique except for the order in which the prime factor occurs.

Euclid’s Division lemma:

           Euclid’s Division lemma can be used to find out the HCF (Highest Common Factor) for any two positive integers for showing the common properties of numbers.

Theorems on rational numbers:

           These are the theorems which satisfies the following properties of rational numbers such as:

  1. The sum of any two rational number is rational
  2. The double of rational number is rational
  3. Every integer is a rational number

Theorems to prove that the number is irrational:

                       These are the theorems which prove that the number is irrational.

      Examples:

  1. Find the mode of the following data:
  • 120,110, 130,110,120,140, 130,120,140,120

         Answer: The mode is 120

  1. Find the largest positive integer that will divide 398, 436, and 542 leaving reminders 7, 11, 15 respectively.

Answer: 17

  1. If p is a prime number, then prove that √p as irrational:

 

  • Algebra:

                 In Term 1 it covers the topics such as Polynomials and Pair of linear equations in two variables whereas in Term 2 it covers the topics such as quadratic equation and arithmetic progression.

Polynomials:

       A polynomial is a mathematical expression that consists of variables and constants combined using addition, multiplication, subtraction and division. The degree of a polynomial is an exponent of the highest degree term.

For example: Constant polynomial is a polynomial of degree 0

                         Liner polynomial is a polynomial of degree 1

                         Quadratic polynomial is a polynomial of degree 2

                         Cubic polynomial is a polynomial of degree 3

       Here the topics such as zeroes of polynomials, relationship between zeroes and coefficient of quadratic polynomials, cubic polynomials, linear polynomials, statement and simple problems on division algorithm, etc.,

Pair of liner equations with two variables:

             A linear equation is an equation of algebraic expression which may consist either constants or variables. Similarly, linear equation for two variables is a form of ax + by + c=0, where x and y are variables, a, b and c are real numbers. The graph of a linear equation of two variables plotted on a Cartesian plane is a straight line.

Quadratic Equations:

           Just like the linear equations are expressed in the form of algebraic expression, a quadratic equation also can be expressed in the form of algebraic expression such as ax2+bx+c=0, where a not equal to zero. This covers the topics such as Roots of quadratic equation, solution of quadratic equation by factorization, solution of quadratic equation by completing the square, formulation of quadratic equation, etc.

Arithmetic progression:

           A sequence of a1, a2, a3…an is said to be an arithmetic progression if there is a constant difference between each successive terms which can be expressed as

A2-a1 = d,

A3-a2= d,

Where d is a common difference.

Examples:

  1. If (y-a) is a factor of f(y) then ______ is a zero of f(y).

Answer: a

  1. Cubic polynomial x=f(y) puts the y-axis at almost

Answer: Three points

  1. Every linear equation in two variables has _______ solutions.

Answer: Infinitely many

  1. Graph of every linear equation in two variables represent a _____

Answer: Straight line

  1. Find two consecutive positive integers, sum of whose squares is 365.

Answer: 13,14

 

  • Geometry:

       This covers the regular topics such as Triangles, circles and construction of geometrical objects.

Triangles:

 A Triangle which is a basic shape of geometry is a polygon with 3 sides and 3 vertices/corners. It is necessary to prove certain conditions in order to prove that two triangles are similar. Conditions such as AAA (Angle-angle-angle), AA (Angle-Angle), SSS (Side-Side-Side) must be satisfied in order to prove two triangles are equal.

Circles:

           A circle is a geometrical object which has no edges or corners. Any circle has a centre point and a circumference. A circumference is a set of all points at a fixed distance from the centre of the circle. Radius of a circle is measured as a distance between the centre of the circle to the circumference of the circle. Diameter of a circle is measured as two times the radius of the circle. Other topics which are covered under this chapter are Tangent of a circle, arc, chord, secant, sector and segments.

Construction of geometrical objects:

                 This is an important branch of Geometry which makes used of specific tools and instruments, specific rules and objects for the construction of Geometrical objects. This chapter covers different ways to construct the 2D objects using compass, ruler and protractor, etc.

       Examples:

  1. The areas of two isosceles triangles are in the ratio 16:25. The ratio of their corresponding heights is_______

Answer: 4 : 5

  1. The inner circumference of a circular track is 440m. The track is 14 m wide. Find the diameter of the outer circle of the track.

Answer: -168

  1. If quadrilateral ABCD is drawn to circumscribe a circle then prove that AB + CD =AD + BC.

 

  • Trigonometry:

         This includes the topics such as Introduction to Trigonometry, Trigonometrical identities, heights and distances in Trigonometry, etc. Trigonometry is a branch of the mathematics which deals with the measurement of angles and sides of a triangle and the problems that comes with the angles. The ratios of the sides of the Triangle with respect to its acute angle are called as Trigonometric ratios. If the trigonometric ratios of an angle of an equation are true for all the values of angle, then it is called as Trigonometric identity.

Examples:

1.The value of cosec 70° – sec 20° is ______

           Answer: 0

  1. A ladder 50 m long just reaches the top of the vertical wall. If the ladder makes an angle of 60 ° with the wall, what is the height of the wall?

           Answer: 25 m

 

  • Statistics and probability:

Statistics:

     There are three measures for central values of a given data such as Mean, Median and Mode. Problems related to Mean, Median and Mode are covered under this syllabus.

Probability:

Probability is a chance of occurrence of a given event. In other words, how likely an event is about to take place. For example, when we toss a coin, the probability of getting either head or tail is 50 %.

Examples:

  1. Questions based on calculating mean, median and mode are covered under the chapter of Statistics.
  2. The probability of an event that is certain to happen is_____

Answer: 1

 

  • Coordinate Geometry:

                 This is a part of geometry which guides to plot a point in the Cartesian plane. A Cartesian plane is a plane with a rectangular coordinate system that associates each point with a pair of numbers which are called as x-coordinate and y-coordinate respectively. X-coordinate measures the distance of the point from the y-axis which is also called as abscissa whereas the y-coordinate measures the distance of the point from the x-axis which is also called as ordinate.

Examples:

  1. What is the distance between the points A(c,0) and B(0,-c)?

Answer: √2 c

  1. Find the point on y-axis which is equidistant from the points (5,-2) and (-3,2).

Answer: (0,-2)

  • Mensuration:

                 This covers the topics such as areas related to the circles, surface areas and volumes, etc.,

Area of circles:

       This covers various topics such as perimeter and area of the circle, area of the sector and segment of the circle, areas of combination of plane figures, etc.,

Surface areas and volumes:

                     Surface area is the total measurement of the surface area covered by all the flat and covered surfaces of 3D objects. Volume is a measure of amount of space occupied by the 3D objects.

Examples:

  1. If the minute hand of a big clock is 1.05 m long, find the rate at which its tip is moving in cm per minute.

Answer: 11cm/min

  1. Find the perimeter of the figure, where AED is a semi-circle and ABCD is a rectangle.

Answer: 76 cm

Thus, these are the syllabus covered in the CBSE Class 10 Mathematics.

 

 

CBSE Class 9 Science Syllabus

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CBSE Class 9 Science :

                         The subject of Science is very important for a growing child since it drives the thinking power among the children. It enhances the skills such as creativity, objectivity, aesthetic sensibility and enquiry. In the primary stage of the school, students observe, draw, record observation and experiment the science subjects, etc.,

In the secondary stage, students are expected to extract ideas from the principles of science subjects, answer quantitative reasoning questions to occupy more central place in the learning and teaching of science.

CBSE Class 9 and 10 syllabuses are divides into two terms such as Term1 and Term 2.

Term 1:

  1. Matter-Its nature and behavior
  2. Organization in living world
  3. Motion, force and work
  4. Food and Food production

Term 2:

  1. Matter-Its nature and behavior (Continued)
  2. Organization in the living world (Continued)
  3. Motion, force and work (Continued)
  4. Our environment

The above syllabus is in detail below:

 

  • Matter-Its nature and behavior:

     This chapter is covered in both first term and second term. Matter is commonly said to exist in four states such as solid, liquid, gas and plasma. In both Physics and Chemistry matter exhibits both wave like and particle like properties which is so called particle duality.

Term 1 covers the topics such as definition of matter, states of matter, characteristics, condensation and sublimation, Nature of matter.

Term 2 covers the topics such as Particle, nature and basic units, mole concepts and structure of atom.

Nature of matter:

               A molecule consists of two or more atoms belonging to the same elements or different elements which are clinically bound together. In this way let us define elements, compounds and mixtures as below;

Elements:

         An element is which cannot be broken down into simpler type of matter by either physical or chemical processes.

Compounds:

             A compound can be broken into simpler types of matter by chemical means and not by physical means.

Mixtures:

         It can be separated into its components by physical means.

Particles, nature and basic units:

                   An atom is the smallest particle which can exist independently and retain its chemical properties. A molecule is also a smallest particle of an element which can also exist independently and can exist even under ordinary conditions.

Structure of atom:

       An atom can be defined as smallest particle of a chemical substance that can exist. An atom consists of sub atomic particles such as neutrons, electrons, and protons. Protons and neutrons form the central core of the atom which is called as nucleus. The electrons revolve around the nucleus in fixed orbits at a great speed.

 

Examples:

  1. What are canal rays?

Answer: E.Goldstein discovered positively charged rays which are called as canal rays.

  1. If an atom contains one electron and one proton, will it carry any charge or not?

Answer: The atom will not contain any charge.

  1. Hydrogen and Oxygen combine in the ratio 1:8 by mass to form water. What mass of oxygen gas would be required to react completely with 3g of hydrogen gas?

Answer: 24 g

  1. Write any two characteristics of particles of matter?

Answer:

  • Particles of matter have a gap between them
  • Particles of matter are continuos in motion
  1. What is a substance?

Answer: A substance can be defined as a matter where constituent particles cannot be separated from each other by any other physical process.

 

  • Organization in living world:

             Just like the first chapter, this chapter is also covered in both term 1 and term 2. In term 1 the topics which are covered are Basic units of life, tissues, organs, organ system, organism, etc. In term 2 the topics which are covered are biological diversity, health and diseases.

Structure and function of cell:

                     All living organisms such as plants, humans and animals are made up of small structures called as cells. If the organism has single cell it is called as single cellular organism whereas if the organism has multiple cell it is called as multi-cellular organism.

Tissues:

               The group of cells performing similar type of functions is called as tissues. These tissues can be classified as plant and animal tissues. Plant tissue can be divided into two types Meristematic, permanent tissue. Animal tissue can be divided into Epethelial tissue, connective tissue, muscular tissue and nervous tissue.

Biological diversity:

                 The biological world can be vastly diversified and classified. Plants or animals can be classified according to their order, family, genus, species, binomial nomenclature.

Health and diseases:

             This chapter deals with various health related topic and diseases caused to the living organisms due to several factors. It covers diseases caused by the microbes, bacteria, virus and the prevention tips to safeguard from those harmful microbes.

Examples:

  1. What is a tissue?

Answer: A group of cells that are same in origin and can perform some specialized function is called as tissue.

  1. In what basis plants and animals are put into different categories?

Answer: On the basis of mode of nutrition

 

  • Motion, force and work:

               In term 1 it covers the topics such as Motion, Newton’s law, force and gravitation. In term 2 it covers floatation, work, energy and power, sound.

Laws of Motion:

       The study of relationships between motion, force and energy is called as mechanics.

Force: Force is a push or pull that can change the current state of motion of an object

Motion: It can be defined as an action or the process of moving or being moved.

Energy: Energy can be defined as the ability to do work or elicit change in matter.

There are three important Newton’s Laws of motion such as below:

First law of motion: This is called as law of inertia. This states that any object will stay in motion until acted upon by an outside force.

Second law of motion: The second law can be defined as Force equals to mass and inertia. F= ma

Third law of motion: For every action there is equal and opposite reaction.

Work, energy, power:

           Work results when a force acts upon the object to cause the displacement. Energy is the capability of doing work. Power is the ability to do something or act in a particular way.

Sound:

       This is a form of energy which comes from the vibrations. These vibrations create sound waves that can travel through the air and water before reaching our ears.

Examples:

  1. Distinguish between speed and velocity?

Answer: Speed is the distance travelled by it per unit time.

Velocity is the displacement per unit time of the body during movement.

  1. From a riffle of mass 4 kg, a bullet of mass 50g is fired with an initial velocity of 35ms-1. Calculate the initial recoil velocity of the riffle.

Answer: v = -0.44m/s

  1. Why sound waves are called as mechanical waves?

Answer: Sound waves need a medium for the propagation. Thus, we can say that they are mechanical waves.

 

  • Food and food production:

         This chapter deals with the importance of food and food production, increase in crop production and animal food.

Improvement in the crop yield:

               The improvement of the crop yield can be made in number of ways by harvesting, weeding crop protection, preparation of qualified soil, harvesting and finally storage.

Food from the animals:

           The breeding, feeding and caring animals for food is called as animal husbandry which includes sericulture, apiculture, pisiculture, poultry farming and livestock farming, etc.,

Examples:

  1. Name few macronutrients?

Answer: Nitrogen, phosphorous, potassium, sulphur, magnesium.

  1. What are the factors responsible for the losses of grains during storage?

Answer: Abiotic fators which are unfavourable conditions of humidity and temperature

Biotic factors are factors such as insects, rodents, bacteria, fungi that feed affect the grains.

 

  • Our environment:

       This chapter is covered in the second term of the CBSE Class 10 Science subject. The topics which are covered under this are Physical resources, bio-geo chemical cycles in nature.

Physical resources:

             Air, water and soil are the physical resources which are very important factors for our environment.

This module explains about the classification, consumption of these resources and factors that deplete our environment.

Examples:

  1. What is the major source of fresh water in village, city and twon?

Answer: Rain water, water from lakes, ponds, pools, dams,etc.,

  1. List any one human activity that may cause air pollution?

Answer: Usage of harmful chemicals such as CFC’s and aerosols.

Thus, the above are the topics which are covered under the syllabus of CBSE Class 9 Science .

CBSE Class 9 Mathematics Syllabus

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CBSE Class 9 Mathematics:

           This is a little higher grade of class which consists of many advanced topics like coordinate geometry, herons formula, Trigonometry, Graphical representation of data, etc., in Mathematics. As per the terms of conditions of CCE (Continuos and Comprehensive Evaluation), the syllabus of CBSE Class 9 and Class 10 has been divided term wise. Each units in both terms will be assessed through Formative and summative assessment. Each term carries two formative assessment each carrying 10% of weightage. It has been declared that the summative assessment for term 1 carries 30% of weightage and summative assessment for the term 2 carries same 30% of weightage.

Let us check the chapters in CBSE Class 9 Mathematics below:

Term 1:

  • Numbers:
  • Geometry
  • Coordinate Geometry
  • Mensuration
  • Algebra

Term 2:

  • Algebra (Continued from Term 1)
  • Geometry (Continued from Term 1)
  • Mensuration (Continued from Term 1)
  • Statistics
  • Probability

Thus, let us see the chapters one by one:

 

  • Numbers:

     As this is the first chapter in all the classes, CBSE Class 9 also includes “Numbers” chapter as the first and foremost chapter. This covers the topics widely as natural numbers, real numbers, rational numbers, terminating / non-terminating recurring decimals, nth root of a real number, etc.

     A set of all rational and irrational numbers are called as real numbers. A number which cannot be represented in the form of p/q, where p and q are integers and q not equal to 0. The decimal expansion of a number is its representation in base 10 of decimal system.

Examples:

  1. The value of 21/3 * 24/3 = ___

Answer: ½

  1. √8 is equal to _______

Answer: 2√2

  1. Find 6 rational numbers between 6/5 and 7/5.

Answer: 61/50,62/50,63/50,64/50,65/50,66/50

 

  • Geometry:

       Just like other classes general topics on Geometry like lines and angles, triangles, circles, quadrilaterals, etc. Another special topic is covered under this chapter which is known as “Euclidean Geometry”. Euclidean Geometry is a mathematical system where geometrical results are proved based on the previously proved results and assumptions called axioms. There are different axioms and theorems based on the Euclidean Geometry.

       In first term, Geometry includes Euclid’s Geometry, Lines & Angles and Triangles whereas in the second term the chapters of Geometry are Quadrilaterals, Area, Circles and construction.

Examples:

  1. The edges of a plane surface:

Answer: Line

  1. Given four points in which no three of them are collinear, then there exists.

Answer: 6 Lines

  1. Which is the correct statement in the following?
  • The line segment has one and only end point
  • Three points are said to be collinear if they lie on the same line
  • Two lines are coincident if they have one point in common
  • The ray AB is same as the ray BA

             Answer: Two lines are said to be collinear if they lie on the same line

  1. Two angles of triangles are 65 degree and 45 degree respectively. Find the third angles.

Answer: 70 degree

  1. Using the Heron’s formula find the area of the triangle whose sides are 3cm, 4cm and 10 cm.

Answer: 24 sq cm

 

  • Coordinate Geometry:

     This is a chapter which deals how to plot a point in a plane when its coordinates are given. The Cartesian plane is a plane with a rectangular coordinate system that associates each point in the plane with a pair of numbers.

     The two numbers are called as x-coordinate which measures the distance of the point from y-axis and y coordinate which measures the distance of the point from the x-axis. This chapter is covered only during the term 1 of CBSE Class 9 Mathematics.

Examples:

  1. The point (0,-5) lies on

Answer: -Ve y-axis

  1. The distance of the point from the (3,0) from the x-axis

Answer: 3 Units

  1. Which of the following points belongs to x-axis?
  • (2,0)
  • (3,3)
  • (0,1)
  • (-2,0)

               Answer: (2,0) and (-2,0) belongs to x-axis

 

  • Mensuration:

   This includes topics such as Area of triangle using Heron’s formula, Area of quadrilateral and its application and so on. This chapter is covered during the term 1 and term 2 of CBSE Class 9 Mathematics.

Examples:

  1. Find the area of Equilateral triangle whose side is 12 cm

Answer: 36√3 sq cm

  1. The perimeter of a Rhombus ABCD is 80 cm. Find the area of the Rhombus if its diagonal BD measures 12 cm.

Answer: 228.8 sq cm

  1. Find the area of isosceles Triangle whose equal sides is 6cm, 6cm and 8 cm.

Answer: 17.8 sq cm

 

  • Algebra:

                 The topics which are covered in the first term of Algebra are Polynomials whereas in the second term it covers Linear equations in two variables. The topics which are covered are definition of polynomials, its coefficients, its counter examples, degree of polynomial, constant, linear, quadrilateral and cubic polynomials. The topics which are covered in the second term are linear equations with one variable, linear equations with two variables, graph of linear equations, etc.

       Examples:

  1. The degree of a constant function is ______

Answer: 0

  1. If x+y+x=0, then x3+y3+z3 is

Answer: 2xyz

  1. Evaluate 105 * 95

Answer: 9975

 

  • Statistics:

           This chapter includes introduction to the statistics, representation of collection of data in a tabular form, ungrouped and grouped charts, bar charts, frequency polygons, mean, median and mode of ungrouped data. This chapter is covered during the second term of CBSE Class Mathematics.

Examples:

  1. What is the upper class limit of the class 37-43?

Answer: 43

  1. What is the class size of the intervals 10-20?

Answer: 10

  1. Find the sum of the deviations from the variety of values 3,4,6,8,14 from their mean.

Answer: 0

  • Probability:

           The probability is a chance of occurrence of a given event which means that how likely that an event can take place. For better understanding, if we toss a coin, the probability of getting either head or tail is 50% chance. The topics which are covered under this chapter are definition of probability, examples of probability, real life examples of probability and so on. This chapter is covered under the second term of CBSE Class 9 Mathematics.

Examples:

  1. What is the probability of a number greater than 6 for a single row of a die?

Answer: 0

  1. A coin is tossed two times. What is the probability of getting two at most 2 heads?
  • ¼
  • ½
  • ¾
  • None of these

             Answer: None of these

  1. A card is drawn from a pack of cards. Find the probability that it is queen?

Answer: 1/13

       Thus, above topics sare the syllabus of CBSE Class 9 Mathematics.

CBSE Class 8 Science Syllabus

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CBSE Class 8 Science:

                 This is a syllabus of elementary standard 8th in CBSE. This covers various topics such as

  1. Food
  2. Materials
  3. The world of living
  4. Moving things, people and ideas
  5. How things work?
  6. Natural Phenomena

 

  • Food:

               This covers various topics under “Food” such as crop production, basic practices in crop production, preparation of soil for cultivation, selection of seeds and sowing techniques, importance of manures and fertilizers, process of irrigation, weeding, harvesting and its importance, methods of storage of water for irrigation, food from animals, microorganisms, etc.

Generally, Agriculture is the cultivation of crops to provide food for all life forms. For such cultivation, soil must be replenished with the nourished manures and fertilizers which can help the seeds to germinate and grow into saplings. Also, enough amounts of other nutrients and water must be supplied at the regular intervals.

Irrigation:

               The proper water supply to the plants according to its type and the season is called as irrigation. There are two types of irrigation such as Traditional irrigation and modern irrigation. Traditional irrigation is the standard method which is done with the help of human labors and animals. This is one of the cheapest irrigation methods which are done with the help of chain pump, moat and rahat. Modern irrigation method is a modern method of supplying water to the crops at the regular interval. This requires solar power or bio gas to automatically sprinkle water to the crops without any wastage.

How to protect the crop?

                Crops are prone to the attacks of pests and insects. Thus, it is necessary to take required steps to protect the crop at the right time. Insects are the six leg organisms which cause heavy loss to the crops whereas pests are the organisms which cause diseases in crop plants. These can be controlled by spraying insecticides and pesticides which can prevent crops from such pests and insects.

Weeding:

   The process of removing waste plants is called as weeding. Weeds If present always compete with the healthy crops in obtaining water, sunlight and nutrients. Thus, it is necessary to remove the weeds or unnecessary crops. Weeding can either be done manually by using harrow before they produce flowers and seeds or it can be tilled along with the soil to kill them. Weeds can also be destroyed by using weedicides which are poisonous to the human beings.

Harvesting:

           The process of cutting the mature crop to gather the grains is called as harvesting. This can either be done manually by using a sickle or using a harvestor.

Threshing:

           It is the process of separating the grains from the straw and chaff. A machine called thresher is used for this purpose.

Winnowing:

         It is the process of natural wind to flow through the grains so that the lighter substances fly away allowing heavier substance falling to the ground.

Animal Husbandry:

                           Breeding and rearing living organisms like cow, goat for the food and other products from them. For example dairy products, poultry farming, pisiculture, sericulture, piggery, etc.,

       Examples:

  1. Give two examples for each type of crops:
  • Kharif crop:
  • Rabi crop:

             Answer:

  • Maize and paddy
  • Wheat and pea
  1. Name the microorganism which can fix the atmospheric nitrogen in the soil.

Answer: Rhizobium, azatobactor, Blue green algae, etc.

 

  • Materials:

       This covers various topics such as Synthetic fibers and plastics, metals and non metals, coal and petroleum, combustion and flame, etc.

Synthetic fibers and plastics:

           There are different types of fibers available such natural and synthetic fibers. Cotton is a natural fiber which is obtained from the cotton plant whereas synthetic fibers are the man-made fibers which are prepared by the many raw materials such as petrochemicals. Synthetic fibers are made up of many small units which combine to form large unit called as a polymer. Plastics are the polymers which consist of very long molecules each composed of carbon atoms linked in chains.

Metals and non-metals:

       Metals are hard, strong and durable which is made used in many machineries, trains, automobiles, aeroplanes, water boiler, etc., However not all metals are hard and strong. Sodium and potassium are soft metals which can be cut with a knife whereas mercury is a liquid. Metals are very good conductors of heat. Non metals exist in three states such as solids, liquids and gas. Non metals do not conduct electricity and heat except graphite.

Coal and petroleum:

                   Animals and plants are drifted down to the earth after their death and decomposed to form peat. Coal was formed due to the compression of peat at high temperature and pressure. Coal is the world’s most abundant fossil fuel. Petroleum is formed from the compressed organic matter which is a dark and oily liquid with an unpleasant odour. As petroleum is lighter than that of water, the deposits of petroleum occur above the water level.

Combustion and flame:

   Combustion is a chemical process which gives off heat when reacting with oxygen. Such substances are called as combustible substances. Example of such substances are LPG, Kerosene, petrol, etc. There are three types of combustion such as rapid combustion, spontaneous combustion and explosion. The substances which vaporizes while burning produced flames. Kerosene oil and molten wax are the substances that give flame while burning. There are two types of flames such as luminous flames and non-luminous flames.

Examples:

  1. Name the petroleum product which can surface the road.

Answer: Bitumen

  1. List the conditions under which combustion can take place?

Answer: Inflammable substance, ignition temperature and Air

  • The world of living:

           These covers the topics such as conservation of plants and animals, cell structure and functions, reproduction in animals, etc.

Conservation of plants and animals:

          Conservation of forest refers to the prevention and maintenance of animals and plants species and protecting them from various threats. Forest can be conserved by maintaining biosphere reserves, wild life sanctuaries, national and zoological parks and botanical gardens.

Cell structure and function:

                     Cell is a structural and functional unit of all living organisms. Every cell in the body is meant to have some basic function. For example, alveolar is an example of single cell. A group of cells which combine to perform similar function is said to be a tissue. A structure of the cell is made up of cell wall, cell membrane, cytoplasm, and the cell organelles.

Cell wall:

               This is present in the structure of a plant cell which gives basic strength and rigidity to the plant body and stands erect during all environmental conditions.

Cell membrane:

           This is a biological membrane which separates interior of the cells from the outside environment.

Cytoplasm:

         It is a jelly like fluid which is present between the nucleus and cell membrane. Cytoplasm is a site of protein synthesis. Almost all metabolic reactions take place in cytoplasm.

Cell organelles:

       These are the living structures which float in the cytoplasm of a cell.

Reproduction in animals:

           This chapter widely covers the topics such as sexual and asexual reproduction in animals, Oviparous and viviparous animals.

Sexual and asexual reproduction in animals:

       Reproduction is a process of developing own species. This can take place in all living organisms such as humans, animals and plants. There are two types of reproduction. They are sexual and asexual reproduction.

Sexual reproduction:

               This type of reproduction involves two organisms such as male and female. Reproductive organs of female produces egg (ovum) whereas the male reproductive organs produce sperm. A zygote is the future individual formed by the fusion of egg and sperm.

Asexual Reproduction:

                 This is a type of reproduction where single parent gives rise to the offspring. Animals reproduce asexually by different process such as binary fission, budding, regeneration, cloning and fragmentation.

Oviparous and viviparous animals:

               Oviparous animals are the animals which can lay eggs. For example: Hen, Frog, Fish, etc., These types of animals undergo external fertilization.

Viviparous animals are the animals which give birth to the young ones. For example, Lion, cat and humans. These types of animals undergo internal fertilization.

Examples:

  1. A place where animals are protected in their natural habitats is called as ________

Answer: Wild life sanctuary

  1. Where does the internal fertilization occur in humans?

Answer: Female body

 

  • Moving things, ideas and people:

    This chapter covers various topics such as force, pressure, friction and sound. Let’s check one by one.

Force:

           An interaction of one object with the other object results in force between two objects. Force has both magnitude and direction. The SI unit of force is Newton.

Pressure:

          Thrust which is a force acted on an object (perpendicular to its surface) acting per unit surface area is called as pressure. The SI unit of pressure is Newton per square meter. (N/m2).

Friction:

   Friction is a type of force which opposes the relative motion between two surfaces of objects in contact.

Sound:

       Sound is a form of energy which causes sensation of hearing. Sound can be heard from all possible objects around us. They are produced from the vibrations caused in the object.

Examples:

  1. Give an example of a situation in which applied force causes a change in the shape of an object.

Answer: Inflated balloon

  1. Sound can travel through _______

Answer: Air, liquids and solids

 

  • How things work?

           This chapter covers topics such as conductivity of liquids and chemical effect of electric current.

Conductivity of liquids:

         Materials through which electric current can pass is called as conductors. Those materials which pass electric current through them are called as good conductors of electricity whereas those materials which do not allow electric current to pass through them are called as bad conductor of electricity.

          Pure water or distilled water is a poor conductor of electricity but if any impurities present in the water, it turns to good conductor of electricity.

Chemical effect of electric current:

           When an electric current is passed through a conducting solution chemical reactions are formed. This is known as chemical effect of electric current. Examples of chemical effects of electric current are:

  • Formation of bubbles of gas on the electrodes
  • Change in the color of solutions
  • Deposition of metals in electrodes

Examples:

  1. When the free ends of the tester are dipped into the solution, the magnetic needle shows the deflection. Why is it so?

Answer: It is because the solution conducts electricity and the solution plays the rule of the cell.

  1. Which of the following cannot be easily charged by friction?
  • A plastic scale
  • A woolen cloth
  • An inflated balloon
  • A Copper rod

 Answer: A copper rod

 

  • Natural Phenomena:

This covers the topic such as Lighting, protection from lightning, earthquakes, etc.,

Lightning:

         Lightning is occurred when friction occurs between water and droplets found in the atmosphere. In other words, lightning is cause due to the heavy electric discharge from the clouds to the earth.

 

Earthquakes:

             A sudden violent shaking of the ground which causes great disaster to the earth.

Examples:

  1. Which of the following is not a green gas?
  • Carbon dioxide
  • Sulphur dioxide
  • Nitrogen
  • Methane

Answer: Sulphur dioxide

  1. State the laws of reflection?

Answer: The angle of incident is equal to the angle of reflection. The ray of incidence, the ray of reflection and the normal point of incidence lie in the same plane.

Thus, the above are the topics which are covered under the CBSE Class 8 Science.

 

CBSE Class 8 Mathematics Syllabus

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CBSE Class 8 Mathematics:

              Just like other CBSE classes, Class 8 has its unique way of structure of syllabus which helps student to understand the topics better. Since the syllabus are designed by the expert teachers, it is always easy for the students at the level of class 8 to understand their topics better.

Lets check out the syllabus of CBSE Class 8 Mathematics below:

 

  • Numbers:

       The chapter “Numbers” covers the syllabus just as that of the previous classes. It includes all basic and important features of “numbers” such as Exponent and powers, rational numbers, even and odd numbers, playing with numbers and factorization. Among this, the newest topics which are added for the CBSE Class 8 level are Square and square root, cube and cube root, playing with numbers, etc.,

Rational numbers:

                 Rational numbers are the numbers which can be expressed in the form of quotient or fraction of two integers. A number is generally said to be a rational number if the numbers in the fraction (for ex) p/q are integers and q is not equal to zero it is said to be a rational number. In other words, it is also expressed as a ratio between two numbers.

Exponents and powers:

                 Exponent can be defined as number of times a number multiplied by itself. Exponents can be expressed as XY where x is a number and y is the power or exponent.

For example, 24 = 2 * 2 * 2 * 2

Squares and square roots:

                 This can be explained as the number raised to the power of 2. In other words, when we multiply a number by itself it is said to be a square of a number. Similarly, a square root of a number x can be explained as the value which when multiplied by itself gives the number x.

For example, 2 is the square root of 4.

Cubes and cube roots:

                 Just like the square root of a number, we can also find out the cube root of a number by just raising the number to the power 3. In other words, the cube root of a number x when multiplied by itself 3 times we get the number x. The topics which are covered under this chapter are Finding the cube of a number, finding cube root of a perfect cubes, cube roots of perfect integers, cube roots of product of integers, cube roots of rational numbers, etc.,

Example for a cube root of 27 = 3 * 3 *3

Playing with numbers:

                This is a chapter which is a fun to solve. This includes topics like finding the patterns of a number, properties and divisibility of a number, a number is said to be divisible by another number when the remainder is zero and so on. Interesting topics which are covered under this chapter are playing Sudoku, magic squares, puzzles, interchanging digits of a number, cryptograms and so on.

        Examples:

  1. Find the multiplicative inverse of 25?

Answer: 1/25

  1. What will be the number of zeroes in the square of 5000?

Answer: 6

  1. Find the square of 39?

Answer: 1521

  1. Find the cube root of 175616.

Answer: 56

  1. What is the rational number that does not have a reciprocal?

Answer: 0

 

  • Algebra:

             A collection of symbols and numbers in an equation and solving them together is called as Algebra. Lot of introduction on Algebra is given in the previous classes and thus in the class 8, advanced concepts like division of algebraic expressions, solving linear equations, etc., are covered.

Identities in Algebra:

               One of the newest topics which has been added in the class 8 is “Identities” of algebra. There are three identities namely

  • Identity 1: Multiplication of monomials
  • Identity 2: Multiplication of a monomial and binomial
  • Identity 3: Multiplication of two binomials

         The other topics which are covered under this chapter are knowing the difference between an equation and identity, multiplication of monomials and polynomials, multiplication of binomials and monomials, etc.,

Factorization:

             Factorization is a process of splitting up an algebraic expression into one or more     factors. Topics which are covered under this are common factors and greatest common factor of monomials, factorization of binomial common factor, factorization of grouping the terms, etc.,

Division of algebraic expression:

                     This covers different topics like division of a monomial with same monomial number, division of polynomial with binomial number, division of polynomial with one variable and division of polynomial by using factorization.

Linear equations:

                         This topic covers introduction to the linear equation, solving linear equation with one variable, finding root of an equation, application and solution of a linear equation, cross multiplication method for solving equations, etc.,

 

Examples:

  1. Solve -36y3 % 9y2 = __

Answer: -4y

  1. In the expression which have the factors of the type (x+a)(x+b), remember the numerical term gives _______

Answer: ab

  1. Which of the following is the monomial?
  • 2x+7
  • 4x +y
  • 3a
  • 3x+5y+7

   Answer: 3a

 

  • Ratio and proportion:

Little advanced problems in ratio and proportion chapter are introduced in class 8. Problems on profit and loss, percentage, discount tax and overhead expenses are covered in this chapter. Other topics which are covered as calculating simple and compound interest, direct variation, inverse variation, time and work problems, etc.

Simple and compound interest:

                     Simple interest means interest calculated on certain amount of money borrowed in a specific period of time. The borrower of the money has to pay back the original principal amount plus the interest amount. It is usually for shorter periods. Compound interest is usually calculated for longer periods. Compound interest is an interest that is added to the principal amount after a specified time period and then the interest is calculated for that new principal amount.

Direct and inverse proportions:

               In a ratio of x:y, if y increases when x increases it is said to be direct proportion whereas y decreases when x increases it is said to be inverse proportion.

Time and work:

                 This is rather an important topic which mainly divided into two variations such as direct and indirect variations. Two variables are said to be “directly variable” if increase in one quantity leads to the corresponding increase in the other quantity. Two variables are said to be “indirectly variable” if increase in one quantity leads to the corresponding decrease in the other quantity.

Examples:

  1. Find the ratio of Rs.6 to 50 paise.

Answer: 12:1

  1. ________ means comparing two quantities.

Answer: Ratio

  1. Write the expression using the exponents: 25 * 25* 25

Answer: 253

  1. The cost of 5 metres of a satin cloth is Rs.210. Find the sot of 15 metres of same type of cloth.

Answer: Rs.630

  1. If 15 workers can build a wall in 48 hours, how many workers are required to do the same work in 30 hours.

Answer: 24

 

  • Geometry:

         As this has become important chapter in the previous classes of CBSE, class 8 covers more important topics under Geometry. This covers various topics like understanding the shapes, properties of different objects like polygon, parallelogram, quadrilateral, etc.,

Understanding polygons:

             A polygon is a closed figure formed by the line segments. There are different types of polygons such as Convex polygon, concave polygon and regular polygon.          

Understanding Quadrilaterals:

           Quadrilateral is a polygon with four sides and four vertices. Examples of polygons are squares, rhombus and trapezium.

Representing 3 dimensional objects in 2 D:

                 This covers various topics such as drawing 2 D objects in 3 Dimensional form, counting vertices, edges, faces and verifying Euler’s relations, etc.,

Examples:

  1. A two dimensional shape is a ______ shape.

Answer: Plane

  1. How many edges are there in a triangular pyramid?

Answer: 6

  1. State the name of the regular polygon of 4 sides.

Answer: Quadrilateral

  1. The diagonals of a _____ are perpendicular bisectors of each other.

Answer: Square

  1. State true of false for the following:
  • All squares are not parallelograms

             Answer: False

  • Mensuration:

           This is calculation of volume, area and perimeter of an object. Total boundary sizes covered by an object is said to be perimeter whereas total surface covered by an object is called as Area. Similarly, total amount of space occupied by the 3-D figure is called as volume. This chapter covers many topics like calculating volume of many 3D objects such as cubes, cuboids, prism, pyramid and others.

Examples:

  1. Find the side of a cube whose surface area is 2400 cm2.

Answer:20 cm

  1. What is the volume of a cuboid?

Answer: L *B * H

 

  • Introduction to graphs:

            Graphs concepts are introduced in this level of CBSE Class 8. Concepts such as axes, Cartesian plane, plotting points from different kinds of situation, reading off from the graphs, reading off linear graphs, reading distance vs time graphs, etc., are covered under this chapter.

Examples:

  1. On which axis does the points (5,0) lie?

Answer: X-axis

  1. In which quadrant does the point P(-8,1) lie?

Answer: IV

Thus, above topics are the syllabus of CBSE Class 8 Mathematics.

CBSE Class 7 Science Syllabus

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CBSE Class 7 Science:

     The syllabus of CBSE Class 7 Science can be divided into many topics such as

  • Food
  • Materials
  • The world of living
  • Moving things, people and ideas
  • Natural Phenomena

These topics in detail are below:

 

  • Food:

       This chapter concentrates on how plants and animals get their food, how do animals utilize their food, types of nutrition, nutrition in amoeba and human beings, etc.,

Nutrients in plants:

         Each and every organism like plants, microbes, animals and humans require nutrients like vitamin, proteins, fat, and carbohydrates in some form. These nutrients help the plants to grow and repair their own damaged parts. Unlike humans and animals, plants obtain their nutrition by various modes such as autotrophic mode or heterotrophic mode. Autotrophic mode is a mode which can synthesize their foods by the process of photosynthesis. Heterotrophic mode is a mode which cannot synthesize their own foods and depend upon other organism for their nutrition.

Nutrition in animals:

             This is widely divided as digestion in animals, digestion in ruminants and digestion in amoeba.

Digestion in animals:

           Animals cannot synthesize their own food and thus depend upon other organisms like plants or other smaller animals for food. Based on the food consumed, the animals can be classified as herbivores, carnivores, and omnivores. Thus animals exhibit heterotrophic mode of nutrition.

Digestion in ruminants:

       Ruminants are nothing but herbivores or grass eating animals. Plants cells contains rich source of cellulose which is an important component in the diet of these herbivores animals. Humans cannot digest this cellulose. The special things about ruminants are, they swallow the food without chewing and then bring it back from the stomach and chew it leisurely.

Digestion in amoeba:

             Amoeba is a microscopic unicellular organism. They are found under the bottom of the fresh waters, ponds, pools, gutters, and in muddy waters. Amoeba is an omnivores organism which feeds on microbes, plants and other smaller organism. Amoeba does not possess any mouth but has a sense of ability to find out which are food particles and which are not. An amoeba engulfs its prey along with a droplet of water in the food vacuole inside the cytoplasm.

Examples:

  1. Why do the organisms need food?

Answer: Organisms need food build their body, get energy, repair and maintain the functions of the body.

  1. State true or false:
  • Digestion of the starch starts in stomach? (T/F)

             Answer: False

 

  • Materials:

                   This chapter covers the topics such as where does our clothing come from, what types of animals are reared to make woolen cloths, What clothes keep us warm, what is heat, temperature, different kinds of materials, classification of substances into acidic, basic and neutral indicators, etc.

Animal fiber-wool and silk:

               Silk is a cloth material which keeps us warm during the winter season. Silk is a product which is extracted from the animal or insect called silkworm. Just like silk, wool is also a cloth material which is extracted from the sheeps and goats. It was the first fibre to run into yarn, and it provides more warmth than any other animal fibres.

Temperature and heat:

         Temperature is a measure of degree of hotness of the body. The SI unit of temperature is Kelvin (K). The instrument that is used to measure the temperature is Thermometer. When an object is at a different temperature than its surroundings, slowly heat transfer takes place turning the object’s temperature same as that of the surroundings. There are three modes of heat transfer such as convection, conduction and radiation.

Acids, bases and Indicators:

       Substances can be classified as acids, bases and neutrals. The chemical nature of any substance which is sour is called as acidic substance. For example: curd

Bases are the substances which taste bitter. They are slippery to touch. For example, soap and lime water. Neutral substance is a substance which does not show acidic or base properties and said to be neutral in nature. Indicators are the substances which are used to test whether the substance is acidic or basic in nature.

Examples:

  1. Ammonium is found in many household products such as window cleaners, etc. It has a nature of turning red litmus to blue. What is the nature of substance called?

             Answer: Basic

  1. Is the distilled water acidic/basic or neutral?

Answer: Neutral

 

  • The world of living:

               This chapter covers the topics such as climate, soil types, adaption of animals to different climate, respiration in plants and animals, herbs, trees and transport of water in trees, excretory system in animals, reproduction system in plants and animals, etc.

Weather and climate:

           The day-to-day conditions of a surrounding atmosphere with the respect to the elements like temperature, heat, moisture, rainfall and wind speed is called as a weather of that place.

          The average weather pattern taken over a long period is called as a climate of that place. There are different types of climates according different places. They are

  • Dry climate
  • Moist tropical climate
  • Humid middle latitude climate
  • Continental climate
  • Cold climate

Winds, Thunderstorms, Cyclones:

         The natural movement of air, generally in a more furious way blowing in a particular direction is called as wind. Thunderstorm is a storm with a thunder and lightning accompanied with heavy rain. They occur due to the convection of air in the hot and humid tropical areas. Cyclone is a natural calamity which is caused due to difference in the air pressure in the atmosphere. It may develop over the sea and may cause severe damages to the land area with a violently rotating wind.

Soil types and its properties:

         Soil is an upper layer of the earth’s crust which is usually composed of a mixture of organic remains, clay and rock particles. There are few important properties of soil such as Absorption of water, moisture in the soil, percolation rate of water in the soil.

Respiration in organisms:

         Respiration is a process of inhaling oxygen and exhaling waste products such as carbon dioxide. It takes place in two types as external respiration and internal respiration. External respiration is also called as breathing which involves inhalation and exhalation. Inhalation is the process of taking in air rich in oxygen whereas exhalation is breathing out air rich in carbon dioxide.

Reproduction in plants:

         Reproduction is a process of developing their offspring or producing their young ones. Reproduction in plants takes place asexually and sexually. Sexual mode of reproduction takes place between two organisms of opposite sex. Reproductive organs in the plants produce gametes-Ovules (Eggs) and pollen grains. Asexual mode of reproduction is a type of reproduction in which single parent is involved to produce the new off spring. In other words, it can be said as growth of new plant from the existing plant other than the seed.

     Examples:

  1. Name the elements that determine the weather of a place?

Answer: Temperature, rainfall and humidity

  1. The water holding capacity is highest in _____type of soil?

Answer: Clayey soil

 

  • Moving things, people and ideas:

       This covers the topics such as time and measurement of time using periodic events and motion of objects.

Time and speed:

       Speed and time can be calculated by a formula such as Speed = Distance / time whereas Time= Distance/ Speed. The SI unit of speed is metre (m) and SI unit of Time is Second. The instruments that are used to measure time is mechanical clocks and simple pendulum.

Graphs:

               A graph is a pictorial representation of given sets of datas. Graph makes clear understanding of the datas given instead of any other form. There are different types of graphs such as bar charts, pie charts, line graphs, etc.,

Examples:

  1. Every object moves with a constant speed? Correct or incorrect?

Answer: Incorrect

  1. A simple pendulum takes 32 s to complete 20 oscillations. What is the time period of the pendulum?

Answer: Time period: 1.6 seconds

 

  • How things work?

     This covers the various topics such as Electric current and its effects, working of an electric bell, a current carrying coil behaves like a magnet, etc.

Electric components:

           There are different electrical components available such as cell, switch, wire, bulb, battery, etc., Different symbols are used to represent different components in an electrical circuit. For example, wire allows to current flow from one part of the circuit to another, similarly switch has an operation called ON or OFF. When switch is off current is not transferred into the electrical circuit. Thus, each electrical component has its own functions to perform.

 

Heating effects of the electric current:

             Naturally when an electric current flows through the wire, the wire gets heated up. This is called as heating effects of the electric current. There are factors such as length and thickness of the wire, material of the wire which may affect heating up of the wire.

 

Magnetic effect of the electric current:

                   When an electric current flows through the wire, the wire behave like a magnet. This is called as magnetic effect of the current. Always a magnetic field is created around the current carrying wire in a given circuit.

 

Examples:

  1. Name any two effects of electric current?

Answer: Magnetic effect

               Heating effect

  1. Do you think that an electromagnet can be used for separating plastic bags from a garbage heap?

Answer: No, electromagnets attract only the magnetic material like iron. So it cannot be used for separating plastic from garbage.

 

  • Natural resources:

           This covers the topics such as scarcity of water, water a precious resource, ways to safeguard water resources, etc.,

 

Water- a precious resource:

                         It is said that nearly 71% of earth is surrounded by water resources such as oceans, sea, lakes, ponds, moisture, humidity, etc., among which most of them are not suitable for the human consumption. Water which is suitable for the human consumption is called as fresh water.

 

By nature, water can exist in three forms such as Solids, liquids and gaseous states.

 

Humans must follow better conservation techniques of water like rain water harvesting system, drip irrigation, bawris, etc.,

 

Importance of forest:

         Forest is a precious resource given by the nature which is area for all types of species forming an ecosystem. Forest areas are the main resources which help in preservation of water on earth. Plants and trees in forest absorb water from the soil through their roots. Thus, it is more necessary to understand the importance of forest and its resources.

 

Examples:

  1. State true or false?
  • The fresh water stored in the ground is much more than that present in the rivers and lakes of the world.

              Answer: True

  1. Herbs from the ______ layer in the forest.

Answer: Ground layer

Thus, these are topics which are covered in the CBSE Class 7 Science.

 

 

CBSE Class 7 Mathematics Syllabus

by

CBSE Class 7 Mathematics:

               The syllabus of CBSE Class 7 Mathematics is an upper primary syllabus for developing the mathematical understanding and interest among the growing children.

The topics which are covered in the CBSE Class 7 are mostly similar to that of class 6. Few of the new topics that are added new in class 7 are Exponents and powers, Congruence of triangle, Triangle and its properties, etc.,

So, let’s check the syllabus of CBSE Class 7 Mathematics below:

 

  • Numbers:

        Just similar to all the previous classes of CBSE, Numbers is the first and foremost chapter in the syllabus of CBSE Class 7 Mathematics. Since this is a upper primary syllabus, Number chapter includes various topics such as

  • Integers
  • Fractions and rational numbers
  • Exponents and powers

      Integers:

                           Integers are the special group of numbers which consists of set of positive and negative    

       whole numbers and do not contain any fractional or decimal part. The syllabus which are covered

       under the topic of “integer” are,

  • Multiplication and Division with integers
  • Addition and subtraction with integers
  • Word problems on integers
  • Properties of integers

       Properties such as Closure property, Commutative, Associative, Distributive are very important properties in the syllabus.

       Examples:

  1. In an exam, positive mark is given for every right answer and negative marks are every wrong answer. If sekar scores 23, 4, -7,-4, 10 in five successive rounds, what is his total at the end?

Answer: 26

  1. When two positive integers are added, we get result in _______

Answer: Positive

Fractions and Rational numbers:

                Fractions can be explained as “number of parts in a whole”. This is represented with a slash. The number above the slash is called as a numerator and the number which is below the slash is called as denominator. Any number which can be represented in a fractional form is called as Rational number. This is represented with “:”. The numerator and denominator are whole numbers in a fraction for a rational number. This includes topics such as multiplication of fraction, fraction as an operator, reciprocal of a fraction, division of a fraction, word problems on mixed fractions and decimal fractions, etc.,

 Examples:

  1. 2 * 1/7 = ___

Answer: 2/7

  1. 3/7*4/11 = ___

Answer: 12/77

  1. Is 1.5 a rational number?

Answer: Yes

Exponents and Powers:

                   Exponent is number of times a number multiplied by itself. This covers different laws of Exponents such as First law, second law up to fifth law. The topics which are covered under this are expressing the number in exponential form, laws of exponent, standard forms of exponent, solving the exponential expressions, expressing decimal number system in exponential form using power of 10, etc.,

Examples:

  1. Simplify the following: (220 % 215) * 25 = _____

Answer: 256

  1. The usual form of 1.001 * 109 = ___

Answer: 1001000000

 

  • Algebra:

         As we already know, introduction to Algebra is given in the previous class 6 and thus this is a continuation of advanced concepts of Algebra. Algebra is a branch of Mathematics which deals with the symbol and rules for manipulating those symbols. The topics which are covered under this chapter are Generating algebraic expressions involving one or two variables, identifying constants, coefficients and powers, addition and subtraction of algebraic expression, simple linear equations in one variable, etc.,

Examples:

  1. Subtract the following:

         3a-b+4 – a –b

Answer: 2a +4

  1. Terms which have same algebraic factors are called as ______

Answer: Like terms

  1. The sum or difference of two like terms is called as ______

Answer: Like term

 

  • Geometry:

   This covers vast topics in Geometry like Lines and Angles, Triangle and its properties, Congruence of Triangle, practical geometry and finding out the perimeter and area.

Lines and Angles:

       A line is a single dimensional object which does not have end point. When two lines meet at a point they form an angle. The point at which the angles are formed is called as vertex. There are different types of angles such as acute angles, adjacent angles, interior angles, exterior angles and so on.

Triangle and its properties:

               Triangle is one of the geometrical shapes which is a polygon with three sides, 3 vertices or 3 corners. There are different types of Triangles such as equilateral triangle, isosceles triangle, scalene triangle and so on. Similarly, each triangle has its own properties such as Angle sum Property of a triangle, Triangle inequality Property and so on. The topics which are covered under this topic are Medians and Altitudes of the Triangles, Exterior angle of a triangle and its properties, Right angled triangle and Pythagoras theorem, sum of the lengths of two sides of a triangle, etc.,

Congruence of a Triangle:

               Two triangles are said to be congruent if their respective angles and sides are equal. This topic covers rules of the congruency of triangles, axioms and so on. The topics which are covered under this are congruence of line segments, angles and plane figures, criteria for congruence of Triangles such as SSS, SAS, ASA, AAS, RHS.

       Examples:

  1. When two angles are supplementary, each angle is said to be ____ of each other.

Answer: Supplement

  1. _____ has no end points.

Answer: Line

  1. According to the Pythagoras property, in a right angled triangle , a square on the ____ = sum of the squares on the legs.

Answer: Hypotenuse

  1. Determine the angle for the following triangle with the sides 3 cm, 4 cm, 5 cm respectively.

Answer: Right angled.

  1. How many medians does a Triangle have?

Answer: Three

  1. An ____ is formed when line segment or lines meet?

Answer: Angle

  1. If two angles have same measurement, then they are said to be ______ angle.

Answer: Congruent

 

  • Collection and Organization of data:

                Collection of data which are represented graphically to understand the structure and organization of the data. This is because it is easier to understand and interpret when it is pictorially represented. Thus, a collection of data can be represented using different types of graphs such as :

  • Bar graphs
  • Tally graphs
  • Pictographs
  • Pie charts

    Examples:

  1. Any type of graphs or charts is given. Questions are based on the given pie chart or bar graph. Answers are solved according to the pictorial representation of data.

 

  • Mensuration:

                 This covers the topics such as finding the perimeter and area of the given object. Perimeter means total boundary size of an object whereas Area is the total surface covered by an object. Different objects such as circle, rhombus, Trapezium are covered under this topic. Topics such as area of rhombus, parallelogram, trapezium, circle, finding the circumference and area of the circle, area between two rectangles and two concentric circles and so on.

        Examples:

  1. Write ¾ in the form of percentage?

Answer: 75%

  1. One fourth of the perimeter of a square gives _____

Answer: Side of the square

  1. What is the area of the parallelogram _____

Answer: Base * Height

 

  • Comparing quantities:

             This covers the new topics such as Profit and loss, calculating percentage and simple interest, etc., This is rather very important chapter for a growing child to understand and calculate this day to day mathematical problems.

Examples:

  1. The cost price of 20 articles is same as the selling price of x articles. If the profit is 25%, then the value of x is:

Answer: 16

  1. If the selling price is doubled, the profit triples. Find the profit percentage?

Answer: 100%

 

  • 3-Dimentional visualization:

               This topic deals with the objects which have three dimensions such as length, height and depth. Examples of such object are sphere, prism, pyramid, cube and cuboid.

Examples:

  1. Which is the three dimensional figure which has six rectangular faces at right angles to each other?

Answer: Cuboid

  1. A three dimensional figure which is bounded by polygons are called as ______

Answer: Polyhedrons

Thus, these are the topics which are covered under the syllabus of CBSE Class 7 Mathematics.

 

 

CBSE Class 6 Mathematics Syllabus

by

CBSE Class 6 Mathematics:

              CBSE Class 6 consists of variety of chapters in Mathematics including all the regular topics introduced in the previous classes. In CBSE Class 6, additional topics which are introduced are

  • Algebra
  • 2 Dimensional and 3 Dimensional Geometrical shapes
  • Perimeter and area of an object
  • Integers
  • Mensuration
  • Practical geometry and construction

The syllabus which are covered under the CBSE Class 6 Mathematics are follows:

 

  • Numbers:

           There are many sub topics covered under the chapter “Numbers”. Topics such as Knowing our numbers, playing with numbers, whole numbers, negative numbers and integers, fractions, etc.,

Knowing our numbers:

            It covers the topics such as comparison of numbers using <.>,+ symbols, ascending and descending order of numbers, calculations of large numbers up to 8 digits, place value of a number, etc.,

Even or odd numbers:

            Integers which are divisible by 2 are said to be even numbers whereas numbers which are not divisible by 2 are said to be odd numbers.

Prime or composite numbers:

             A natural number which has only two distinct factors which is “1” and the number itself, is said to be a prime number. A number other than “1” and not a prime number is said to be a composite number.

Relatively prime or co-prime numbers:

             A set of numbers which do not have any common factor other than “1”, are said to be co-prime numbers or relatively prime number.

Perfect Numbers:

              Perfect numbers are the natural numbers, whose sum of positive divisors (except the number itself) is equal to the number itself.

Playing with numbers:

             It is part of mathematics which is fun to solve. It involves concepts such as even, odd numbers, prime and composite numbers, divisibility rules, multiple and factors, prime factorization, HCF and LCM and simplification of brackets.

Negative numbers and integers:

            Importance of negative numbers, arranging the negative numbers in ascending and descending order, introduction to integers, how to solve the problem with integers, how to solve the problems involving addition and subtraction of integers, etc.,

Whole numbers:

           Whole numbers are a set of positive integers. They do not have any fractional or decimal part. Natural numbers along with zero are whole numbers. This topic covers the concepts such as natural numbers, whole numbers, properties of numbers such as commutative, associative, distributive, multiplicative identity, additive identity), solving problems involving whole numbers, knowing the difference between whole numbers and natural numbers, etc.,

Fractions:

           Fractions and decimals are the most important chapters in “Numbers”. Fractions are the representation of a number with “/” whereas decimal is the representation of a number with “.”(Decimal point).

Examples:

  1. 783422 _____ 783426
  • > 
  • < 
  • =
  • None

             Answer: <

  1. What is the predecessor of 3456?
  • 3455
  • 3478
  • 3422
  • 3498

             Answer: 3455

  1. If the product of two whole numbers is zero, then ________ of them will be zero.

Answer: one

  1. _____ is the factor of 50
  • 10
  • 3
  • 7
  • 6

           Answer: 10

  1. Fourth multiple of 8 is ___
  • 16
  • 24
  • 32
  • 40

           Answer: 32

 

  • Introduction to Algebra:

       Algebra is an important branch of Mathematics which is introduced right from the CBSE Class 6th level. Algebra can be defined as a part of mathematics which deals with the symbols and rules for manipulating those symbols. The main concept in Algebra is “Equations”. Every equation in algebra describes the relationship between two variables. Any equation has two parts in LHS and RHS with “=” in between. The topics which are covered under this are recognizing the Algebraic expression, expressing an algebraic equation, introduction to different terms of expression, solving algebraic expression, etc.,

Examples:

  1. Find out the expression with numbers only?
  • 2y+5
  • (20%5) -3z
  • 3x+3
  • 3(23-5)+5*2

               Answer: 3(23-5)+5*2

  1. An equation has ____ sides with = sign between LHS and RHS.
  • Two
  • Three
  • Four
  • Six

               Answer: Two

 

  • Ratio and Proportion:

         Ratios are the concepts which are used to compare two values. They make us understand the difference between two numbers. If total number of boys in a class is 5 and total girls in that class is 4, then the ratio of boys in the class can be represented as 5/9. Proportion is a name which is given when two ratios are equal. This can be represented as a:b=c:d. The above topics covers the syllabus such as ratio and proportion of a number, unitary method and word problems based on Ratio and proportion.

Examples:

  1. Meetu weight is 25 kg and her mother’s weight is 75 kg. What is the ratio of weight of meetu to weight of her mother?
  • 1:3
  • 1:2
  • 1:4
  • 3:1

             Answer: 1:3

  1. If two ratios are equal then we say that they are ______

Answer: Proportional

 

  • Geometry:

         This topic covers concepts such as Basic 2 dimensional geometrical ideas, understanding elementary shapes (2 dimensional and 3 dimensional), symmetry and construction of Geometrical objects.

Examples:

  1. How many end points does a ray have?
  • 0
  • 2
  • 3
  • 1

           Answer: 1

  1. The end points of same sides of a polygon are called the _______ vertices.
  • Parallel
  • Same
  • Different
  • Adjacent

             Answer: Adjacent

 

  • Mensuration:

           Already students would have learned about the basic concepts of finding the perimeter, area of a given object in the previous classes.

Perimeter is the total number of boundary size that an object can cover whereas area is the total number of surface that an object covers. The other concepts which are covered under this topic are concept of Area, area of a rectangle and triangle, calculating the perimeter of a rectangle and square.

Examples:

  1. Find the perimeter of a regular octagon with each side measuring 3 cm.
  • 24 cm
  • 20 cm
  • 10 cm
  • 15 cm

             Answer: 24 cm

  1. Find the side of the square whose perimeter is 20 m.
  • 4 m
  • 3 m
  • 6 m
  • 5 m

             Answer: 5 m

 

  • Practical Geometry and construction:

                 This is a branch of Geometry which deals with the construction of geometrical objects. There are specific instruments or tools and specific rules to construct the geometrical objects. The tools such as ruler, compass, protractor can be used to construct every geometrical object.

               The topics which are covered under this are construction of line segment using ruler and compass, construction of circle, construction and measuring angles, construction of perpendicular bisector, how to bisect angles, etc.,

Examples:

  1. Find out the correct type of the triangle which has sides 7 cm, 8 cm and 9 cm.
  • Isosceles triangle
  • Scalene Triangle
  • Equilateral triangle
  • None of these

               Answer: Scalene Triangle

  1. The measure of right angle is ____
  • 60 degree
  • 90 degree
  • 180 degree
  • 30 degree

             Answer: 90 degree

 

  • Statistics and data handling:

         Collection of information is said to be data. These data can be pictorially represented using graphs, charts, bar charts, etc. The reason behind representing the data through pictorial representation is it gives a clear understanding of the data and its organization. Graphs such as pictographs, tally graphs, bar charts and pie charts are used to represent the data.

        The topics which are covered under the “Statistics and Data Handling” are definition of data, construction of pictograph, collection and organizing data using the charts such as bar charts, interpret data using the pictograms and graphs.

Examples:

  1. A _____ represents data through pictures of objects.

Answer: Pictograph

  1. The _______ each bar gives required information.

Answer: Length

 

  • 3 D shapes:

                 This covers the topics such as 3 dimensional shapes and sizes of an object, recognizing different 3d shapes, understanding the concepts of vertices, edges and faces , etc.,

Examples:

  1. A _______ is a polygon with four sides.

Answer: Quadrilateral

  1. Two faces meet at a line segment called as ______

Answer: Edge

Thus, the above topics are covered under the syllabus of CBSE Class 6 Mathematics.

 

 

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